2,550 research outputs found
Laplace operators on differential forms over configuration spaces
Spaces of differential forms over configuration spaces with Poisson measures
are constructed. The corresponding Laplacians (of Bochner and de Rham type) on
forms and associated semigroups are considered. Their probabilistic
interpretation is given
Remarks on some new models of interacting quantum fields with indefinite metric
We study quantum field models in indefinite metric. We introduce the modified
Wightman axioms of Morchio and Strocchi as a general framework of indefinite
metric quantum field theory (QFT) and present concrete interacting relativistic
models obtained by analytical continuation from some stochastic processes with
Euclidean invariance. As a first step towards scattering theory in indefinite
metric QFT, we give a proof of the spectral condition on the translation group
for the relativistic models.Comment: 13 page
A hierarchical model of quantum anharmonic oscillators: critical point convergence
A hierarchical model of interacting quantum particles performing anharmonic
oscillations is studied in the Euclidean approach, in which the local Gibbs
states are constructed as measures on infinite dimensional spaces. The local
states restricted to the subalgebra generated by fluctuations of displacements
of particles are in the center of the study. They are described by means of the
corresponding temperature Green (Matsubara) functions. The result of the paper
is a theorem, which describes the critical point convergence of such Matsubara
functions in the thermodynamic limit.Comment: 24 page
p-Adic Schr\"{o}dinger-Type Operator with Point Interactions
A -adic Schr\"{o}dinger-type operator is studied.
() is the operator of fractional differentiation and
is a singular potential containing the Dirac delta
functions concentrated on points of the field of
-adic numbers . It is shown that such a problem is well-posed
for and the singular perturbation is form-bounded for
. In the latter case, the spectral analysis of -self-adjoint
operator realizations of in is carried
out
Many Body Problems with "Spin"-Related Contact Interactions
We study quantum mechanical systems with "spin"-related contact interactions
in one dimension. The boundary conditions describing the contact interactions
are dependent on the spin states of the particles. In particular we investigate
the integrability of -body systems with -interactions and point spin
couplings. Bethe ansatz solutions, bound states and scattering matrices are
explicitly given. The cases of generalized separated boundary condition and
some Hamiltonian operators corresponding to special spin related boundary
conditions are also discussed.Comment: 13 pages, Late
From Stochastic Differential Equations to Quantum Field Theory
Covariant stochastic partial (pseudo-)differential equations are studied in
any dimension. In particular a large class of covariant interacting local
quantum fields obeying the Morchio-Strocchi system of axioms for indefinite
quantum field theory is constructed by solving the analysed equations. The
associated random cosurface models are discussed and some elementary properties
of them are outlined.Comment: 11 pages, Latex, to appear in: Reports On Mathematical Physics No.X
Vol.XX (199X
On Integrability and Pseudo-Hermitian Systems with Spin-Coupling Point Interactions
We study the pseudo-Hermitian systems with general spin-coupling point
interactions and give a systematic description of the corresponding boundary
conditions for PT-symmetric systems. The corresponding integrability for both
bosonic and fermionic many-body systems with PT-symmetric contact interactions
is investigated.Comment: 7 page
Dispersive estimate for the Schroedinger equation with point interactions
We consider the Schroedinger operator in R^3 with N point interactions placed
at Y=(y_1, ... ,y_N), y_j in R^3, of strength a=(a_1, ... ,a_N). Exploiting the
spectral theorem and the rather explicit expression for the resolvent we prove
a (weighted) dispersive estimate for the corresponding Schroedinger flow.
In the special case N=1 the proof is directly obtained from the unitary group
which is known in closed form.Comment: 12 page
Symmetry, Duality and Anholonomy of Point Interactions in One Dimension
We analyze the spectral structure of the one dimensional quantum mechanical
system with point interaction, which is known to be parametrized by the group
U(2). Based on the classification of the interactions in terms of symmetries,
we show, on a general ground, how the fermion-boson duality and the spectral
anholonomy recently discovered can arise. A vital role is played by a hidden
su(2) formed by a certain set of discrete transformations, which becomes a
symmetry if the point interaction belongs to a distinguished U(1) subfamily in
which all states are doubly degenerate. Within the U(1), there is a particular
interaction which admits the interpretation of the system as a supersymmetric
Witten model.Comment: 47 pages, 5 figures (with 7 EPS files); corrected typo
On the stability of one particle states generated by quantum fields fulfilling Yang-Feldman equations
We prove that for a Wightman quantum field the assumptions (i)
positivity of the metric on the state space of the theory (ii) the
asymptotic condition in the form of Yang-Feldman equations and (iii)
Klein-Gordon equation for the outgoing field imply that the states generated by
application of the asymptotic fields to the vacuum are stable. We prove by a
counter example that this statement is wrong in the case of quantum fields with
indefinite metric
- âŠ