相关论文: Mode regularization, time slicing, Weyl ordering a…

This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…

We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the…

The use of the dimensional regularization in the on-mass-shell renormalization scheme sometimes fails to locally cancel the ultraviolet divergence for a class of diagrams in the two-loop order. The mechanism is discussed based on an example…

The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them,…

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…

A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…

We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of $d$, $N\times N$ matrices invariant under the adjoint action of the symmetric…

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators (which considers normal ordered, antinormally ordered and Weyl…

Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…

We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…

We study a quantum system in a Riemannian manifold M on which a Lie group G acts isometrically. The path integral on M is decomposed into a family of path integrals on a quotient space Q=M/G and the reduced path integrals are completely…

This work addresses the quantization of a self-interacting higher order time derivative theory using path integrals. To quantize this system and avoid the problems of energy not bounded from below and states of negative norm, we observe the…

We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical…

In quantum field theory, sharp momentum states have to be normalized to be in Fock space. We investigate different normalization schemes, both box normalization and wave packets. These methods are equivalent in flat spacetimes, but turn out…

In this work we present a derivation of Dirac's equation in a curved space-time starting from a Weyl-invariant action principle in 4+K dimensions. The Weyl invariance of Dirac's equation (and of Quantum Mechanics in general) is made…

The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…

We present a family of non-local variational regularization methods for solving tomographic problems, where the solutions are functions with range in a closed subset of the Euclidean space, for example if the solution only attains values in…

Quantum computers are expected to scale in size to close the gap that currently exists between quantum algorithms and quantum hardware. To this end, quantum compilation techniques must scale along with the hardware constraints, shifting the…

It is a common belief among field theorists that path integrals can be computed exactly only in a limited number of special cases, and that most of these cases are already known. However recent developments, which generalize the WKBJ method…

Regularisation theory in Banach spaces, and non--norm-squared regularisation even in finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable to the extension of first-order optimisation…