Related papers: Path Integral for Non-Paraxial Optics
Path integral approaches have been used for boson and fermion systems. The path integral approach has been successful in the many-boson system. However, in the many-fermion system, the path integral approach is not feasible due to the sign…
By taking the Weyl equation with external electro-magnetic potentials as the simplest representative for a system of PDOs, we give a new method of treating non-commutativity of coefficients matrices. More precisely, we construct a Fourier…
We introduce a new method for evaluating the oscillatory integrals which describe natural interference patterns. As an illustrative example of contemporary interest, we consider astrophysical plasma lensing of coherent sources like pulsars…
It is discussed an opportunity to introduce new class of quantum algorithms based on possibility to express amplitude of transition between two states of quantum system as sum of some function along all possible classical paths. Continuous…
In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a…
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in $D$ dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action…
The standard derivation of Schroedinger's equation from a Lorentz-invariant Feynman path integral consists in taking first the limit of infinite speed of light and then the limit of short time slice. In this order of limits the light cone…
I review the generating function for quantum-statistical mechanics, known as the Feynman-Vernon influence functional, the decoherence functional, or the Schwinger-Keldysh path integral. I describe a probability-conserving $i\varepsilon$…
The derivation of the Feynman path integral based on the Trotter product formula is extended to the case where the system is in a magnetic field.
We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined by the absorbing boundary. Trajectories that reach the absorbing wall are…
The saddle points of a conventional Feynman path integral are not entangled, since they comprise a sequence of classical field configurations. We combine insights from field theory and tensor networks by constructing a Feynman path integral…
The Feynman Path Integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
Integration By Parts (IBP) is an important method for computing Feynman integrals. This work describes a formulation of the theory involving a set of differential equations in parameter space, and especially the definition and study of an…
We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $k=0,+1,-1$ are considered. To construct the path integrals in the timeless framework, a…
In the path integral formulation of the partition function of quantum spin models, most current treatments employ the so-called static approximation to simplify the process of summing over all possible paths. Although sufficient for…
We develop a systematic projector-based Feynman diagram framework that intrinsically encodes quantum geometry for nonlinear optical responses. By explicitly incorporating geometric quantities such as the quantum geometric tensor, quantum…
We discuss the formulation of spin observables associated to a non-relativistic spinning particles in terms of grassmanian differential operators. We use as configuration space variables for the pseudo-classical description of this system…
The concept of the PT-symmetry, originating from the quantum field theory, has been intensively investigated in optics, stimulated by the similarity between the Schr\"odinger equation and the paraxial wave equation that governs the…
The Feynman path integral does not allow a "one real path" interpretation, because amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, "all paths happen", is not a useful or informative account. In this…