相关论文: A Phase Space Path Integral for (2+1)-Dimensional …

We compare three approaches to the quantization of (2+1)-dimensional gravity with a negative cosmological constant: reduced phase space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of…

Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…

The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…

The previous discussion \cite{ezawa} on reducing the phase space of the first order Einstein gravity in 2+1 dimensions is reconsidered. We construct a \lq\lq correct" physical phase space in the case of positive cosmological constant,…

We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…

While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and…

An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…

We work out the phase-space functional integral of the gravitational field in 2+1 dimensions interacting with N point particles in an open universe.

We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is…

Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…

Using a regularised construction of the phase space path integral due to Ingrid Daubechies and John Klauder which involves a time scale ultimately taken to vanish, and motivated by the general programme towards a noncommutative space(time)…

Quantum tunneling in a many-body system is much more non-trivial than that in a one-body system. The most characteristic phenomenon is the mixed tunneling, which has been studied in many fields for decades. For instance, let us consider a…

We derive the geometric quantization program of symplectic manifolds, in the sense of both Kostant-Souriau and Weinstein, from Feynman's path integral formulation on phase space. The state space we use contains states with negative norm and…

We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…

Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the…

The prerequisites of the extended phase space approach to quantization of gravity, which is alternative to the Wheeler-DeWitt one and other existing approaches, are presented. The features of the proposed approach and conclusions from its…

In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of…

The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…

Phase-space path-integrals are used in order to illustrate various aspects of a recently proposed interpretation of quantum mechanics as a gauge theory of metaplectic spinor fields.

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…