Related papers: Schroedinger Self-adjoint Extension and Quantum Fi…
The present work proves that the folk-lore of the pathology of non-conservation of probability in quantum anisotropic models is wrong. It is shown in full generality that all operator ordering can lead to a Hamiltonian with a self-adjoint…
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to…
By using the spherical coordinates in 3+1 dimensions we study the self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an infinitely thin magnetic flux tube. It is shown that the angular part of the Dirac Hamiltonian…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
In a previous paper [\AS], we used superspace techniques to prove that perturbation theory (around a classical solution with no zero modes) for Chern--Simons quantum field theory on a general $3$-manifold $M$ is finite. We conjectured (and…
We consider a generalization of the non-Hermitian ${\mathcal PT}$ symmetric Jaynes-Cummings {Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay}.…
Interacting electrons in a semiconductor quantum dot at strong magnetic fields exhibit a rich set of states, including correlated quantum fluids and crystallites of various symmetries. We develop in this paper a perturbative scheme based on…
Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in…
We develop the quantum theory of the causal formation of a long-range magnetic field generated by an external current that is instantaneously switched on and subsequently kept constant in time. The resulting non-equilibrium quantum state,…
We consider a 1-parameter family of self-adjoint extensions of the Hamiltonian for a particle confined to a finite interval with perfectly reflecting boundary conditions. In some cases, one obtains negative energy states which seems to…
This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of…
The problem of construction a quantum mechanical evolution for the Schrodinger equation with a degenerate Hamiltonian which is a symmetric operator that does not have self-adjoint extensions is considered. Self-adjoint regularization of the…
Using the method of implementable one-particle Bogoliubov transformations it is possible to explicitly define a local covariant net of quantum fields on the (universal covering of the) circle $S_1$ with braid group statistics. These Anyon…
Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics.…
We give an exposition of how the Kauffman bracket arises for certain systems of anyons, and do so outside the usual arena of Temperley-Lieb-Jones categories. This is further elucidated through the discussion of the Iwahori-Hecke algebra and…
We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for $n$-point functions. Perturbation theory leads us to…
It is shown that the perturbative expansions of the correlation functions of a relativistic quantum field theory at finite temperature are uniquely determined by the equations of motion and standard axiomatic requirements, including the KMS…
We study $1+1$-dimensional $\text{SU}(N)$ gauge theory coupled to one adjoint multiplet of Majorana fermions on a small spatial circle of circumference $L$. Using periodic boundary conditions, we derive the effective action for the quantum…
A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum…
We establish a new self-consistent system of equations accounting for a non-minimal interaction of gravitational, electromagnetic and axion fields. The procedure is based on a non-minimal extension of the standard Einstein-Maxwell-axion…