相关论文: Functional Integral Representation for Relativisti…
In this paper the Hamiltonian for the system of semi-relativistic particles interacting with a scalar bose field is investigated. A scaled total Hamiltonian of the system is defined and its scaling limit is considered. Then the…
The gauge symmetry group of any slave boson representation allows to gauge away the phase of bosonic fields. One benefit of this radial field formulation is the elimination of spurious Bose condensations when saddle-point approximation is…
The system of semi-relativistic particles coupled to a scalar Bose field is considered. A scaled total Hamiltonian for the system is a self-adjoint operator on a tensor product of a square-integrable function space and a boson Fock space.…
We study the quasi-classical limit of the Pauli-Fierz model: the system is composed of finitely many non-relativistic charged particles interacting with a bosonic radiation field. We trace out the degrees of freedom of the field, and…
We consider an interaction representation in the Boltzmann field theory. It describes the master field for a subclass of planar diagrams in matrix models, so called half-planar diagrams. This interaction representation was found in the…
A Feynman-Kac-type formula for a L\'evy and an infinite dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation of $e^{-t\PF}$ generated by the…
We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means…
Path integral representations for generalized Schr\"odinger operators obtained under a class of Bernstein functions of the Laplacian are established. The one-to-one correspondence of Bernstein functions with L\'evy subordinators is used,…
The quantum system of a massless charged scalar field with a self-interaction is investigated. By introducing a spacial cut-off function, the Hamiltonian of the system is realized as a linear operator on a boson Fock space. It is proven…
The authors reexamine the two-dimensional model of massive fermions interacting with a massless pseudoscalar field via axial-current-pseudoscalar derivative coupling. Performing a canonical field transformation on the Bose field algebra the…
Schrodinger equation with two-component wave function which describes a relativistic spin 1/2 particle in a weak electromagnetic field is obtained. In the same approximation Schrodinger equation with traditional norm condition and…
A number of results on radial positive definite functions on ${\mathbb R^n}$ related to Schoenberg's integral representation theorem are obtained. They are applied to the study of spectral properties of self-adjoint realizations of two- and…
By means of functional integrations spectral properties of semi-relativistic Pauli-Fierz Hamiltonians in quantum electrodynamics is considered. Two self-adjoint extensions of a semi-relativistic Pauli-Fierz Hamiltonian are defined. An…
We write the Hamiltonian of the Bose gas with two-body repulsive $\delta$-function potential in a pseudoparticle operator basis which diagonalizes the problem via the Bethe ansatz. In this operator basis the original bosonic interactions…
For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by…
The composite system, formed by two $S=1$ particles, is considered. The field operators of constituents are transformed on the $(1,0)\oplus (0,1)$ representation of the Lorentz group. The problem of interaction of $S=1$ particle with the…
In this paper, we use the theory of fractional powers of linear operators to construct a general (analytic) representation theory for the square-root energy operator of relativistic quantum theory, which is valid for all values of the spin.…
Recently, a functional integral representation was proposed by Weller (Weller, W.: phys.~stat.~sol.~(b) {\bf 162}, 251 (1990)), in which the fermionic fields strictly satisfy the constraint of no double occupancy at each lattice site. This…
We present a general derivation of semi-fermionic representation for generators of SU(N) group as a bilinear combination of Fermi operators. The constraints are fulfilled by means of imaginary Lagrange multipliers. The important case of…
Radial slave boson representations have the particular advantage that the expectation values of their respective fields are finite even without the formal introduction of spurious Bose condensates for each of the bosonic fields. The…