Related papers: Non-standard phase space variables, quantization, …
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…
Path integrals can be rigorously defined only in low dimensional systems where the small distance limit can be taken. Particularly non-trivial models in more than four dimensions can only be handled with considerable amount of speculation.…
The path integral formulation introduced in [arXiv:2210.12761] "Path integrals, particular kinds, and strange things" by Friston and colleagues in 2023, offers an innovative lens for examining complex systems, particularly through its…
We discuss a path integral formalism to introduce noncommutative generalizations of spacetime manifold in even dimensions, which have been suggested to be reasonable effective pictures at very small length scales, of the order of Planck…
We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description…
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…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.
We characterize all the phase space measurements for a non-relativistic particle.
The kinematic degrees of freedom of spinning particles are analyzed and an explicit construction of the phase space and the simplectic structure that accomodates them is presented. A Poincare invariant theory of classical spinning particles…
Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
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.
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the…
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…
A method for nonperturbative path integral calculation is proposed. Quantum mechanics as a simplest example of a quantum field theory is considered. All modes are decomposed into hard (with frequencies $\omega^2 >\omega^2_0$) and soft (with…
A short tutorial on non-standard analysis, made in particular for people working in the Categorical Quantum Mechanics crowd.
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…