# Theoretical and Mathematical Physics

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 101-117

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 1-1

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 41-60

_{g}AU*

_{g}= g(A) on Dom(A), where A is a densely defined operator and G ∋ g ↦ U

_{g}is a unitary representation of the subgroup G of the affine group

*G*, the group of affine orientation-preserving transformations of the real axis. If A is a symmetric operator, then the group G induces an action/flow on the operator unit ball of contracting transformations...

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 83-92

_{0}and σ

_{1}and the set σ

_{1}is in a finite gap of the set σ

_{1}. It is known that if V is a bounded additive self-adjoint perturbation of A that is off-diagonal with respect to the partition spec(A) = σ

_{0}∪ σ

_{1}, then for $$\left\| V \right\| < \sqrt 2 d$$ , where d = dist(σ...

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 21-40

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 126-135

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 118-125

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 61-69

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 70-82

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 93-100

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 136-146

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 2-20

Theoretical and Mathematical Physics > 2016 > 186 > 2 > 148-155

Theoretical and Mathematical Physics > 2016 > 186 > 2 > 205-212

*D*-dimensional (

*D*≥ 3) space–time. We show that the interaction energy regularized by dimensional regularization contains neither ultraviolet divergences nor divergences associated with the nonintegrable nature of the vacuum mean of the energy–momentum tensor operator. In the case of four space–time...

Theoretical and Mathematical Physics > 2016 > 186 > 2 > 286-293

Theoretical and Mathematical Physics > 2016 > 186 > 2 > 183-191

Theoretical and Mathematical Physics > 2016 > 186 > 2 > 192-204

*є*-expansions (

*τ*-series) for the critical exponents of a

*λϕ*

^{4}-type three-dimensional

*O*(

*n*)-symmetric model obtained on the basis of six-loop renormalization-group expansions. We present numerical results in the physically interesting cases

*n*= 1,

*n*= 2,

*n*= 3, and

*n*= 0 and also for 4 ≤

*n*≤ 32 to clarify the general properties of the obtained series. The pseudo-

*є*-expansions or the...

Theoretical and Mathematical Physics > 2016 > 186 > 2 > 231-250

^{2}. The Schrödinger operator

*H*(

*k*

_{1},

*k*

_{2}) of the system for

*k*

_{1}=

*k*

_{2}=

*π*, where

**k**= (

*k*

_{1},

*k*

_{2}) is the total quasimomentum, has an infinite number of eigenvalues. In the case of a special potential, one eigenvalue is simple, another one is double, and the other eigenvalues have multiplicity three. We prove that the double eigenvalue...

Theoretical and Mathematical Physics > 2016 > 186 > 2 > 268-279

*H*(

*ε*),

*ε*> 0. We prove that for a sufficiently small

*ε*> 0, this operator has no bound states and no two-particle branches of the spectrum. We also obtain an estimate for the small parameter

*ε*.

Theoretical and Mathematical Physics > 2016 > 186 > 2 > 156-182