The spin of a free electron is stable but its position is not. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have shown that the Feynman position path integral can be mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). Since the more common use of MUBs is in finite dimensional Hilbert spaces, this raises the question “what happens when spin path integrals are computed (...) over products of MUBs?” Such an assumption makes spin no longer stable. We show that the usual spin-1/2 is obtained in the long-time limit in three orthogonal solutions that we associate with the three elementary particle generations. We give applications to the masses of the elementary leptons. (shrink)

Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of entangled states as entities in a high-dimensional Hilbert space, or the intuitive view of these states as a connection between distant spatial configurations, it may not even be obvious that a path-based calculation can be achieved using only paths in ordinary space and time. (...) Previous work has shown how to do this for certain special states; this paper extends those results to all pure two-qubit states, where each qubit can be measured in an arbitrary basis. Certain three-qubit states are also developed, and path integrals again reproduce the usual correlations. These results should allow for a substantial amount of conventional quantum analysis to be translated over into a path-integral perspective, simplifying certain calculations, and more generally informing research in quantum foundations. (shrink)

This paper argues that the path integral formulation of quantum mechanics suggests a form of holism for which the whole (total ensemble of paths) has properties that are not strongly reducible to the properties of the parts (the single trajectories). Feynman’s sum over histories calculates the probability amplitude of a particle moving within a boundary by summing over all the possible trajectories that the particle can undertake. These trajectories and their individual probability amplitudes are thus necessary in calculating the (...) total amplitude. However, not all possible trajectories are differentiable, thus suggesting that they are not physical possibilities, but only mathematical entities. It follows that if the possible differentiable trajectories are taken to be part of the physical system, they are not sufficient to calculate the total probability amplitude. The conclusion is that the total ensemble is weakly non-supervenient upon the physically possible trajectories. (shrink)

Williams (WS) and Down (DS) syndromes are neurodevelopmental disorders with distinct genetic origins and different spatial memory profiles. In real-world spatial memory tasks, where spatial information derived from all sensory modalities is available, individuals with DS demonstrate low-resolution spatial learning capacities consistent with their mental age, whereas individuals with WS are severely impaired. However, because WS is associated with severe visuo-constructive processing deficits, it is unclear whether their impairment is due to abnormal visual processing or whether it reflects an inability (...) to build a cognitive map. Here, we tested whether blindfolded individuals with WS or DS, and typically developing (TD) children with similar mental ages, could use path integration to perform an egocentric homing task and return to a starting point. We then evaluated whether they could take shortcuts and navigate along never-traveled trajectories between four objects while blindfolded, thus demonstrating the ability to build a cognitive map. In the homing task, 96% of TD children, 84% of participants with DS and 44% of participants with WS were able to use path integration to return to their starting point consistently. In the cognitive mapping task, 64% of TD children and 74% of participants with DS were able to take shortcuts and use never-traveled trajectories, the hallmark of cognitive mapping ability. In contrast, only one of eighteen participants with WS demonstrated the ability to build a cognitive map. These findings are consistent with the view that hippocampus-dependent spatial learning is severely impacted in WS, whereas it is relatively preserved in DS. (shrink)

The action for a massive particle in special relativity can be expressed as the invariant proper length between the end points. In principle, one should be able to construct the quantum theory for such a system by the path integral approach using this action. On the other hand, it is well known that the dynamics of a free, relativistic, spinless massive particle is best described by a scalar field which is equivalent to an infinite number of harmonic oscillators. We (...) clarify the connection between these two—apparently dissimilar—approaches by obtaining the Green function for the system of oscillators from that of the relativistic particle. This is achieved through defining the path integral for a relativistic particle rigorously by two separate approaches. This analysis also shows a connection between square root Lagrangians and the system of harmonic oscillators which is likely to be of value in more general context. (shrink)

The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its invariance properties under variations of the action. These relations determine a dynamical algebra of bounded operators which encodes all properties of the corresponding quantum theory. This novel approach is applied to non-relativistic particles, where quantum mechanics emerges from it. The method works also (...) in interacting quantum field theories and sheds new light on the foundations of quantum physics. (shrink)

We summarize the essential ingredients, which enabled us to derive the path-integral for a system of harmonically interacting spin-polarized identical particles in a parabolic confining potential, including both the statistics (Bose–Einstein or Fermi–Dirac) and the harmonic interaction between the particles. This quadratic model, giving rise to repetitive Gaussian integrals, allows to derive an analytical expression for the generating function of the partition function. The calculation of this generating function circumvents the constraints on the summation over the cycles of (...) the permutation group. Moreover, it allows one to calculate the canonical partition function recursively for the system with harmonic two-body interactions. Also, static one-point and two-point correlation functions can be obtained using the same technique, which make the model a powerful trial system for further variational treatments of realistic interactions. (shrink)

Barut's classical model of the spinning particle having external dynamical variables x and p and internal dynamical variables $\bar z$ and z is taken into account. The path integrations over holomorphic spinors $\bar z$ and z are discussed. This quantization gives the kernel of the relativistic particles with higher spin as well as the Dirac electron. The Green's function of the spin-n/2 particle is obtained.

The proposal made 50 years ago by Schulman :1558–1569, 1968), Laidlaw and Morette-DeWitt :1375–1378, 1971) and Dowker to decompose the propagator according to the homotopy classes of paths was a major breakthrough: it showed how Feynman functional integrals opened a direct window on quantum properties of topological origin in the configuration space. This paper casts a critical look at the arguments brought by this series of papers and its numerous followers in an attempt to clarify the reason why the (...) emergence of the unitary linear representation of the first homotopy group is not only sufficient but also necessary. (shrink)

The concept of “transaction,” introduced by Cramer in his realistic nonlocal interpretation of quantum mechanics (QM), is herein reformulated in the language of the Feynman graphs' technique.

In this paper, I explore the feasibility of a realistic interpretation of the quantum mechanical path integral - that is, an interpretation according to which the particle actually follows the paths that contribute to the integral. I argue that an interpretation of this sort requires spacetime to have a branching structure similar to the structures of the branching spacetimes proposed by previous authors. I point out one possible way to construct branching spacetimes of the required sort, and I ask (...) whether the resulting interpretation of quantum mechanics is empirically testable. (shrink)

For time-independent fields the Aharonov-Bohm effect has been obtained by idealizing the coordinate space as multiply-connected and using representations of its fundamental homotopy group to provide information on what is physically identified as the magnetic flux. With a time-dependent field, multiple-connectedness introduces the same degree of ambiguity; by taking into account electromagnetic fields induced by the time dependence, full physical behavior is again recovered once a representation is selected. The selection depends on a single arbitrary time (hence the so-called holonomies (...) are not unique), although no physical effects depend on the value of that particular time. These features can also be phrased in terms of the selection of self-adjoint extensions, thereby involving yet another question that has come up in this context, namely, boundary conditions for the wave function. (shrink)

The (Feynman) propagator G(x2,x1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G(x_2,x_1)$$\end{document} encodes the entire dynamics of a massive, free scalar field propagating in an arbitrary curved spacetime. The usual procedures for computing the propagator—either as a time ordered correlator or from a partition function defined through a path integral—requires introduction of a field ϕ(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi (x)$$\end{document} and its action functional A[ϕ(x)]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A[\phi (...) (x)]$$\end{document}. An alternative, more geometrical, procedure is to define a propagator in terms of the world-line path integral which only uses curves, xi(s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^i(s)$$\end{document}, defined on the manifold. I show how the world-line path integral can be reinterpreted as an ordinary integral by introducing the concept of effective number of quantum paths of a given length. Several manipulations of the world-line path integral becomes algebraically tractable in this approach. In particular I derive an explicit expression for the propagator GQG(x2,x1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_\mathrm{QG}(x_2,x_1)$$\end{document}, which incorporates the quantum structure of spacetime through a zero-point-length, in terms of the standard propagator Gstd(x2,x1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_\mathrm{std}(x_2,x_1)$$\end{document}, in an arbitrary curved spacetime. This approach also helps to clarify the interplay between the path integral amplitude and the path integral measure in determining the form of the propagator. This is illustrated with several explicit examples. (shrink)

In the transdisciplinary field of ‘mindfulness,’ originally a Buddhist concept (Pāli sati; Sanskrit smṛti; Chinese nian 念; Tibetan dran pa), the two tendencies represented by Buddhist traditional a...

The path integral is not typically utilized for analyzing entanglement experiments, in part because there is no standard toolbox for converting an arbitrary experiment into a form allowing a simple sum-over-history calculation. After completing the last portion of this toolbox (a technique for implementing multi-particle measurements in an entangled basis), some interesting 4- and 6-particle experiments are analyzed with this alternate technique. While the joint probabilities of measurement outcomes are always equivalent to conventional quantum mechanics, differences in the calculations (...) motivate a number of foundational insights, concerning nonlocality, retrocausality, and the objectivity of entanglement itself. (shrink)

From the very beginning, coherent state path integrals have always relied on a coherent state resolution of unity for their construction. By choosing an inadmissible fiducial vector, a set of “coherent states” spans the same space but loses its resolution of unity, and for that reason has been called a set of weak coherent states. Despite having no resolution of unity, it is nevertheless shown how the propagator in such a basis may admit a phase-space path integral (...) representation in essentially the same form as if it had a resolution of unity. Our examples are toy models of similar situations that arise in current studies of quantum gravity. (shrink)

Hamilton-Jacobi theory is applied to find appropriate canonical transformations for the calculation of the phase-space path integrals of the relativistic particle equations. Hence, canonical transformations and Hamilton-Jacobi theory are also introduced into relativistic quantum mechanics. Moreover, from the classical physics viewpoint, it is very interesting to find and to solve the Hamilton-Jacobi equations for the relativistic particle equations.

We study here the properties of some quantum mechanical wave functions, which, in contrast to the regular quantum mechanical wave functions, can be predetermined with certainty (probability 1) by performing dense measurements (or continuous observations). These specific “certain” states are the junction points through which pass all the diverse paths that can proceed between each two such neighboring “sure” points. When we compare the properties of these points to the properties of the well-known universal wave functions of Everett we find (...) a strong similarity between these two apparently uncorrelated entities, and in this way find the same similarity between the Feynman path integrals and Everett's universal wave functions. (shrink)

Recent studies of the contribution made by the hippocampus to spatial behavior suggest that it plays a role in integrating and double integrating distance and direction information using cues generated by self-movement. This and other evidence that the hippocampus plays a central role in spatial behavior seems inconsistent with proposals that it is primarily involved in episodic memory.

In an accompanying paper Gomes, we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe M, existing on timeless configuration space \ of some field over M. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. Locality in full can only emerge dynamically, and is not postulated. This new understanding of locality is based solely on (...) the properties of extremal paths in configuration space. I do not demand locality from the start, as it is usually done, but showed conditions under which certain systems exhibit it spontaneously. In this way we recover semi-classical local behavior when regions dynamically decouple from each other, a notion more appropriate for extension into quantum mechanics. The dynamics of a sub-region O within the closed manifold M is independent of its complement, \, if the projection of extremal curves on \ onto the space of extremal curves intrinsic to O is a surjective map. This roughly corresponds to \, where \ is a linear projection. This criterion for locality can be made approximate—an impossible feat had it been already postulated—and it can be applied for theories which do not have hyperbolic equations of motion, and/or no fixed causal structure. When two regions are mutually independent according to the criterion proposed here, the semi-classical path integral kernel factorizes, showing cluster decomposition which is the ultimate aim of a definition of locality. (shrink)

The unified treatment of the Dirac monopole, the Schwinger monopole, and the Aharonov-Bohm problem by Barut and Wilson is revisited via a path integral approach. The Kustaanheimo-Stiefel transformation of space and time is utilized to calculate the path integral for a charged particle in the singular vector potential. In the process of dimensional reduction, a topological charge quantization rule is derived, which contains Dirac's quantization condition as a special case. “Everything that is made beautiful and fair and lovely (...) is made for the eye of one who sees.” Jelaluddin Rumi,Mathnawi [I, 2383]. (shrink)

Starting from the earlier notions of stationary action principles, these tutorial notes shows how Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. Part I brings out in more detail the connection between the two formulations, and applications are discussed. Then, the Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.

We formalize the notion of isolated objects, and we build a consistent theory to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time reversal condition on the whole set of indistinguishable paths of a unit, we show that the quantization of motion of spinless (...) elementary particles in a general potential field can be derived in this framework, in the limiting case of weak fields and low velocities. Extrapolating this approach to include weak relativistic effects, we explore possible experimental consequences. We conclude by suggesting a primitive ontology for the theory of isolated objects. (shrink)

This article describes the path‐mapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lower‐level retrieval of analogous role paths, and coordinate mappings with higher‐level organizational knowledge. Implemented in the ACT‐R cognitive architecture, the path‐mapping theory enables models of analogical mapping behavior to incorporate and interface with other problem‐solving knowledge. Path‐mapping models thus can include task‐specific skills such as encoding analogs or generating (...) responses, and can make behavioral predictions at the level of real‐world metrics such as latency or correctness. We show that the path‐mapping theory can successfully account for the major phenomena addressed by previous theories of analogy. We also describe a path‐mapping model that can account for subjects' incremental eye‐movement and typing behavior in a story‐mapping task. We discuss extensions and implications of this work to other areas of analogy and problem‐solving research. (shrink)

The traditional ideological and political education should keep pace with the times, and the physical and health education should highlight its value, and must combine the two. This study investigated on the integration path of mental health education and college students’ ideological and political education. A stratified random sampling was conducted on 2021 students of a higher vocational college. The subjects were divided into the control group and the experimental group. The experimental group was given the integrated intervention course (...) of mental health education and ideological and political education of college students, and the control group was given routine teaching. The depression score of the experimental group is significantly lower than that of the control group, and the mental health quality score is higher than that of the control group. Contribution: The integration of mental health education and college students’ Ideological and political education can effectively improve the level of college students’ mental health. This course constantly improves the students’ subjective consciousness, subjective ability and subjective personality, and fully reflects the educational effect of the ideological and political education of college students’ mental health course. This research provides data which could be utilised by academics in the field of practical theology, especially youth ministry and religious educational studies. (shrink)

The Hooks et al. review of microbiota-gut-brain literature provides a constructive criticism of the general approaches encompassing MGB research. This commentary extends their review by: highlighting capabilities of advanced systems-biology “-omics” techniques for microbiome research and recommending that combining these high-resolution techniques with intervention-based experimental design may be the path forward for future MGB research.

A propagator for a path space integral can be used to represent the and provides a natural way to model a control signal that is temporally segmented by placement of pairs of stimulating and recording electrodes. Although care must be exercised in interpreting the resulting measurement, the technique should prove useful to experimenters who study cerebellar functioning.

Scientific integrity is defined as the condition that occurs when individuals adhere to accepted standards, professional values, and practices of the relevant scientific community. This study aims to investigate the influential factors on the scientific integrity in scholarly publishing of researchers in Thailand. The questionnaire was delivered to a sample size of 398 top researchers who had high citations and h-index recorded in the Scopus database during the past 5 years, 316 responses were returned. The findings confirm that there are (...) five factors that affect scientific integrity in scholarly publishing: university/faculty requirements/policies, university support, aspects of publishing, publisher aspects, and researcher-related factors. It is evident that establishing a process and criteria for authorship agreement and verification, as well as dedicating offices or units within the university to address research integrity concerns and provide support to researchers, exhibit the highest factor loading values. The findings ensure that scientific integrity stands out as a top priority for researchers linked with prominent research universities in Thailand. To tackle this challenge, it is recommended for the universities to prioritize initiatives aimed at enhancing researchers’ ethical awareness and nurturing scientific integrity. (shrink)

Searching for better ways to inspire people to pursue wisdom, Frederick D. Aquino argues that teachers and researchers should focus less on state-of-the-art techniques and learning outcomes and instead pay more attention to the intellectual formation of their students. We should, Aquino contends, encourage the development of an integrative habit of mind, which entails cultivating the capacity to grasp how various pieces of data and areas of inquiry fit together and to understand how to apply this information to new situations. (...) To fully explore this notion, _An Integrative Habit of Mind_ brings the work of the great religious figure and educator John Henry Newman into fruitful conversation with recent philosophical developments in epistemology, cognition, and education. Aquino unearths some crucial but neglected themes from Newman’s writings and carries them forward into the contemporary context, revealing how his ideas can help us broaden our horizons, render apt judgments, and better understand our world and how we think about it. (shrink)

I argue that it is through an integrative dialogue based on the Ijing model of cooperative and cyclical change rather, than a Marxist or neo-Marxist dialectical model of change based upon the Hegelian model of conflict and replacement, that promises the greatest possibility of peaceful coexistence. As a case study of a dialogue between civilizations, I utilize both a mythical and an historical encounter between Martin Buber, representing the West, and Zhuangzi, representing the East. I show that despite the vast (...) temporal, historic, linguistic and cultural differences, that the dialogue between Zhuangzi and Buber is complementary and not adversarial. (shrink)

_The Lamp that Integrates the Practices_ is a systematic and comprehensive exposition of the most advanced yogas of the Esoteric Community Tantra as espoused by the Noble Tradition, an influential school of interpretation within the Mahayoga traditions of Indian Buddhist esoterism. Equal in authority to Nagarjuna's famous Five Stages, Aryadeva's work is perhaps the earliest prose example of the "stages of the mantra path" genre in Sanskrit. Its studied gradualism exerted immense influence on later Indian and Tibetan tradition, and (...) it is widely cited by masters from all four major lineages of Tibetan Buddhism. This volume presents the _Lamp_ in a tri-lingual format: its Sanskrit original critically-edited from recently-identified manuscripts, a critical edition of the eleventh-century Tibetan translation by Rin-chen Bzang-po, and a thoroughly-annotated English translation. Includes an introductory study discussing the history of the Guhyasamaja and its exegetical traditions, surveying the scriptural and commentarial sources of the Noble Tradition, and analyzing in detail the contents of the _Lamp_. Features a detailed, tri-lingual glossary. Published by American Institute of Buddhist Studies. (shrink)