Related papers: Proper time and path integral representations for …
An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to…
Quantum field theory in curved spacetimes suffers in general from an infinite ambiguity in the choice of Fock representation and associated vacuum. In cosmological backgrounds, the requirement of a unitary implementation of the field…
Light-cone formulation of conformal field theory in space-time of arbitrary dimension is developed. Conformal fundamental and shadow fields with arbitrary conformal dimension and arbitrary spin are studied. Representation of conformal…
We show that the emergence of time evolution in an otherwise timeless nonrelativistic closed quantum system -- viewed as a poor man's model of generally covariant quantum theory -- can be understood from the perspective of the path integral…
We write down an explicit projection that maps any given 4-spinor to a point in 3+1 spacetime while commuting with the Lorentz action. This suggests that a Lorentz invariant theory - including spacetime itself - has a more natural…
The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are…
The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for…
We discuss the path integral representation for the fermionic particles and strings and concentrate at the problems arising when some target-space dimensions are compact. An example of partition function for fermionic particle at finite…
A variation to the usual formulation of Grassmann representation path integrals is presented. Time-indexed anticommuting partners are introduced for each Grassmann coherent state variable and a general method for handling the effect of…
The path-integral quantization of thermal scalar, vector and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and $\phi ^4$ theory as examples. By this quantization,…
We construct and study singular functions in strong-field $QED$ with two external electromagnetic fields that represent principally different types of external backgrounds, the first one belongs to the class of so-called $t$-potential…
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…
We propose a classical constrained Hamiltonian theory for the spin. After the Dirac treatment we show that due to the existence of second class constraints the Dirac brackets of the proposed theory represent the commutation relations for…
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 discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum…
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…
Field equations in four order derivatives with respect to time and space coordinates based on modified classic relativistic energy of the fractal theory of time and space are received. It is shown appearing of new spin characteristics and…