Related papers: General Solution of Quantum Master Equation in Fin…
A general method for the construction of solutions of the d'Alambertian and double d'Alambertian (harmonic and bi-harmonic) equations with local dependence of arbitrary functions upon two independent arguments is proposed. The connection…
This work makes progress on the issue of global vs. local master equations. Global master equations like the Redfield master equation (following from standard Born and Markov approximation) require a full diagonalization of the system…
We develop a theory of existence and uniqueness of solutions of MFG master equations when the initial condition is Lipschitz continuous. Namely, we show that as long as the solution of the master equation is Lipschitz continuous in space,…
String-local fields constitute a relatively new tool for solving quantum field theory, stressing and embodying locality and positivity. We examine here their usefulness -- as well as some drawbacks. Starting from just the physical masses…
This letter studies the Sp(2) covariant quantisation of gauge theories. The geometrical interpretation of gauge theories in terms of quasi principal fibre bundles $Q(M_S, G_S)$ is reviewed. It is then described the Sp(2) algebra of ordinary…
We discuss the locality problem in relativistic and nonrelativistic quantum theory. We show that there exists a formulation of quantum theory that, on one hand, preserves the mathematical apparatus of the standard quantum mechanics and, on…
In the framework of theory of open quantum systems, we derive quantum master equations for the ultrastrong system-bath coupling regime and, more generally, the strong-decoherence regime. In this regime, the strong decoherence is…
In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of…
We argue that the conventional quantum field theory in curved spacetime has a grave drawback: The canonical commutation relations for quantum fields and conjugate momenta do not hold. Thus the conventional theory should be denounced and the…
We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be universal if it contains a quadratic subform that is…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
The multidimensional gravity on the total space of principal bundle is considered. In this theory the gauge fields arise as nondiagonal components of multidimensional metric. The spherically symmetric and cosmology solutions for gravity on…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
The status of locality in quantum mechanics is analyzed from a nonstandard point of view. It is assumed that quantum states are relative, they depend on and are defined with respect to some bigger physical system which contains the former…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
By introducing the generalized master function of order up to four together with corresponding weight function, we have obtained all quasi-exactly solvable second order differential equations. It is shown that these differntial equations…
We generalize the spherical harmonics for l=1 and give the differential equation that the generalized forms satisfy. The new forms have an obvious interpretation in the context of quantum mechanics.
Modular localization and the theory of string-localized fields have revolutionized several key aspects of quantum field theory. They reinforce the contention that local symmetry emerges directly from quantum theory, but global gauge…
The quantum theory of a free particle in two dimensions with non-local boundary conditions on a circle is known to lead to surface and bulk states. Such a scheme is here generalized to the quantized Maxwell field, subject to mixed boundary…
We consider equations of the type: \[\partial_t \omega = \omega R(\omega),\] for general linear operators $R$ in any spatial dimension. We prove that such equations almost always exhibit finite-time singularities for smooth and localized…