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Yu. S. Vernov

Publications and source records attributed to Yu. S. Vernov.

14 recordsLinked to original sources
arXiv2019

Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. II

Classical results of the axiomatic quantum field theory, namely the irreducibility of the set of field operators, Reeh and Schlieder's theorems and generalized Haag's theorem, are proven in $SO(1,1)$ invariant quantum field theory, of which an important example is noncommutative quantum field theory. New consequences of generalized Haag's theorem are obtained in $SO(1,3)$ invariant theories. It has been proven that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories.

hep-th↗
arXiv2012

Haag's Theorem in Noncommutative Quantum Field Theory

Haag's theorem was extended to noncommutative quantum field theory in a general case when time does not commute with spatial variables. It was proven that if S-matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in another theory is equal to unity as well. In fact this result is valid in any SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory.

math-ph↗
arXiv2011

Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory

We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space-time. These Wightman functions involve the $\star$-product among the fields, compatible with the twisted Poincaré symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ($θ_{0i}=0$), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.

hep-th↗
arXiv2011

Haag's theorem in S O (1, k) invariant quantum field theory

Generalized Haag's theorem has been proved in S O (1, k) invariant quantum field theory. Apart from the above mentioned k+1 variables there can be arbitrary number of additional coordinates including noncommutative ones in the theory. New consequences of generalized Haag's theorem are obtained. It has been proved that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories. In space-space noncommutative quantum field theory in four-dimensional case it has been proved that if in one of the theories under consideration S-matrix is equal to unity, then in another theory S-matrix is unity as well.

math-ph↗
arXiv2010

Rigorous Definition of Quantum Field Operators in Noncommutative Quantum Field Theory

The space, on which quantum field operators are given, is constructed in any theory, in which the usual product between test functions is substituted by the $\star$-product (the Moyal-type product). The important example of such a theory is noncommutative quantum field theory (NC QFT). This construction is the key point in the derivation of the Wightman reconstruction theorem.

math-ph↗
arXiv2004

Jost-Lehmann-Dyson Representation, Analyticity in Angle Variable and Upper Bounds in Noncommutative Quantum Field Theory

The existence of Jost-Lehmann-Dyson representation analogue has been proved in framework of space-space noncommutative quantum field theory. On the basis of this representation it has been found that some class of elastic amplitudes admits an analytical continuation into complex \cos\vartheta plane and corresponding domain of analyticity is Martin ellipse. This analyticity combined with unitarity leads to Froissart-Martin upper bound on total cross section.

hep-th↗
arXiv2003

Analyticity and Forward Dispersion Relations in Noncommutative Quantum Field Theory

We derive the analytical properties of the elastic forward scattering amplitude of two scalar particles from the axioms of the noncommutative quantum field theory. For the case of only space-space noncommutativity, i.e. $θ_{0i}=0$, we prove the dispersion relation which is similar to the one in commutative quantum field theory. The proof in this case is based on the existence of the analog of the usual microcausality condition and uses the Lehmann-Symanzik-Zimmermann (LSZ) or equivalently the Bogoliubov-Medvedev-Polivanov (BMP) reduction formalisms. The existence of the latter formalisms is also shown. We remark on the general noncommutative case, $θ_{0i}\neq0$, as well as on the nonforward scattering amplitude and mention their peculiarities.

hep-th↗