Related papers: Necessity of integral formalism
The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total…
The distinctive features of quantum mechanics, which set it apart from other physical theories, challenge our notions of realism. Recovering realism from purely philosophical grounds, a quantitative and operational criterion was proposed in…
In calculations on quantum state-resolved dynamics of a chemical reaction, reactants are usually prepared in separated eigenstates of individual fragments, and their direct-product is then evolved in time. In this work, we focus on the…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…
A new methodology of simulating nonadiabatic dynamics using frozen-width Gaussian wavepackets within the moving crude adiabatic representation with the on-the-fly evaluation of electronic structure is presented. The main feature of the new…
We study infrared divergences in quantum electrodynamics using geometric phases and the adiabatic approximation in quantum field theory. In this framework, the asymptotic \textit{in} and \textit{out} states are modified by Berry phases,…
Experimentally feasible methods to determine the Berry phase, a fundamental quantity characterizing a quantum material, are often needed in applications. We develop an approach to detecting the Berry phase by using a class of…
When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber bundle, the independence of the formal path…
In the present study we attempt to incorporate the philosophical dialogue about physical reality into the instructional process of quantum mechanics. Taking into account that both scientific realism and constructivism represent, on the…
We introduce a perturbative approach to solving the time dependent Schroedinger equation, named adiabatic perturbation theory (APT), whose zeroth order term is the quantum adiabatic approximation. The small parameter in the power series…
We propose a novel method to describe realistically ionization processes with absorbing boundary conditions in basis expansion within the formalism of the so-called Non-Adiabatic Quantum Molecular Dynamics. This theory couples…
The Berry phase acquired by an electromagnetic field undergoing an adiabatic and cyclic evolution in phase space is a purely quantum-mechanical effect of the field. However, this phase is usually accompanied by a dynamical contribution and…
We demonstrate that the existence of a Hermitian time-dependent intertwining operator that maps the non-Hermitian time-dependent energy operator to its Hermitian conjugate and its right to its left eigenstates guarantees the reality of the…
Three out of four complex components of the Dirac spinor can be algebraically eliminated from the Dirac equation (if some linear combination of electromagnetic fields does not vanish), yielding a partial differential equation of the fourth…
We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
At present there are two vastly different ab initio approaches to the description of the the many-body dynamics: the Density Functional Theory (DFT) and the functional integral (path integral) approaches. On one hand, if implemented…
The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of…
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…