相关论文: A New Look At The Path Integral Of Quantum Mechani…

I offer some historical comments about the origins of Feynman's path integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's…

We investigate the Poisson-Sigma model on the classical and quantum level. In the classical analysis we show how this model includes various known two-dimensional field theories. Then we perform the calculation of the path integral in a…

Geometric quantization of 2+1 dimensional pure Yang-Mills theory is studied with focusing on finite large scales. It is previously shown that (Yildirim, 2015, Int. J. Mod. Phys A, 30(7), 1550034), topologically massive Yang-Mills theory…

We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…

It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also…

The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…

We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4,…

Normally we quantize along the space dimensions but treat time classically. But from relativity we expect a high level of symmetry between time and space. What happens if we quantize time using the same rules we use to quantize space? To do…

For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…

A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…

This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields…

The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed…

We show that the computational effort for the numerical solution of fermionic quantum systems, occurring e.g., in quantum chemistry, solid state physics, field theory in principle grows with less than the square of the particle number for…

Tremendous ongoing theory efforts are dedicated to developing new methods for QCD calculations. Qualitative rather than incremental advances are needed to fully exploit data still to be collected at the LHC. The maximally supersymmetric…

We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the…

By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which…

The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…

Power duality in Feynman's path integral formulation of quantum mechanics is investigated. The power duality transformation consists of a change in coordinate and time variables, an exchange of energy and coupling, and a classical angular…

Feynman's path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes $ K(x^{"},t^{"};x',t')$ for two-dimensional systems with quadratic Lagrangians are evaluated analytically and…

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.…