Related papers: Quantum propagator for some classes of three-dimen…
We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.
Here we examine the propagation of relativistic fields in spacetime using the viewpoint applied to derive the Rayleigh--Sommerfeld diffraction integral in three--dimensional space. We use this theory to find the propagators for both the…
Feynman propagator is calculated for the time dependent harmonic oscillator by converting the problem into a free particle motion
The coherent transfer of excitations between different locations of a quantum many-body system is of primary importance in many research areas, from transport properties in spintronics and atomtronics to quantum state transfer in quantum…
We discuss the general three-particle quantum scattering problem, for motion restricted to the full line. Specifically, we formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As a…
We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…
In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…
We study aspects of the quantum and classical dynamics of a $3$-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual…
We investigate the behavior of the one body propagator in SQED. The self energy is calculated using three different methods: i) the simple bubble summation, ii) the Dyson-Schwinger equation, and iii) the Feynman-Schwinger represantation.…
We derive the complete list of singularities of propagators in theories with arbitrary (complex) masses and for arbitrary diagram. We derive in a closed form differential equations for the propagator as a function of the momentum and…
New types of relationships between Feynman integrals are presented. It is shown that Feynman integrals satisfy functional equations connecting integrals with different values of scalar invariants and masses. A method is proposed for…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
In the path integral formulation of quantum mechanics, the phase factor Exp[iS(x[t])] is associated with every path x[t]. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
We derive the fixed-$\Lambda$ and unimodular propagators using the path integral formalism as applied to the Einstein-Cartan action. The simplicity of the action (which is linear in the lapse function) allows for an exact integration…
We propose to include gravity in quantum field theory non-perturbatively, by modifying the propagators so that each virtual particle in a Feynman graph move in the space-time determined by the four-momenta of the other particles in the same…
The evolution equation for the propagator of the quantum system in the optical probability representation (optical propagator) is obtained. The relations between the optical and quantum propagators for the Schr\"odinger equation and the…
The quantum Dirac-like equation and the QED vertex operator for a composite particle are suggested. The vertex operator and the fermionic propagator are connected by the QED Ward identity. It is shown that all of the Feynman QED-integrals…
The symmetries of a scalar field theory in multifractional spacetimes are analyzed. The free theory realizes the Poincar\'e algebra, and the associated symmetries are modifications of ordinary translations and Lorentz transformations. In…