Related papers: Path integral for minisuperspaces and its relation…
We employ the path integral approach developed in [29] to discuss the (generalized) harmonic oscillator in a noncommutative plane. The action for this system is derived in the coherent state basis with additional degrees of freedom. From…
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical…
The main purpose of this paper is to present a new approach to logic or what we will call superlogic. This approach constitutes a new way of looking at the connection between quantum mechanics and logic. It is a {\it geometrisation} of the…
We investigate a canonical way of defining bisimilarity of systems when their semantics is given by a coreflection, typically in a category of transition systems. We use the fact, from Joyal et al., that coreflections preserve open…
A path-integral quantization on a homogeneous space G/H is proposed based on the guiding principle `first lift to G and then project to G/H'. It is then shown that this principle gives a simple procedure to obtain the inequivalent…
Quantum entanglement is the quintessence of quantum information processing mostly limited to the microscopic regime governed by Heisenberg uncertainty principle. For practical applications, however, macroscopic entanglement gives great…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
We investigate the hitherto unexplored relation between the superparticle path integral and superfield theory. Requiring that the path integral has the global symmetries of the classical action and obeys the natural composition property of…
A theorem that constructs a path integral solution for general second order partial differential equations is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
We discuss a recent approach to quantum field theoretical path integration on noncommutative geometries which imply UV/IR regularising finite minimal uncertainties in positions and/or momenta. One class of such noncommutative geometries…
The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries:…
An analysis using a composition of currently-accepted theories is given. Starting with a synthesis of what may be generically termed ``paths'', analysis of representations for these ``paths'' is developed. Foreground and background…
I study several aspects of the path(st) integral we formulated in previous papers on energetic causal sets with Cortes and others. The focus here is on quantum field theories, including the standard model of particle physics. I show that…
In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification problems of homogeneous and isoparametric hypersurfaces, polar…
It is known that the quantization of a system defined on a topologically non-trivial configuration space is ambiguous in that many inequivalent quantum systems are possible. This is the case for multiply connected spaces as well as for…
Regge calculus minisuperspace action in the connection representation has the form in which each term is linear over some field variable (scale of area-type variable with sign). We are interested in the result of performing integration over…
Theories that contain first class constraints possess gauge invariance which results in the necessity of altering the measure in the associated quantum mechanical path integral. If the path integral is derived from the canonical structure…
We develop parallel transport on path spaces from a differential geometric approach, whose integral version connects with the category theoretic approach. In the framework of 2-connections, our approach leads to further development of…
We study the relationship between quasihomotopy and path homotopy for Sobolev maps between manifolds. We employ singular integrals on manifolds to show that, in the critical exponent case, path homotopy implies quasihomotopy - and observe…