Scenario for the renormalization in the 4D Yang-Mills theory
The renormalizability of the Yang-Mills quantum field theory in four-dimensional space-time is discussed in the background field formalism.
hep-th↗
arXiv subjects
L. D. Faddeev
Publications and source records attributed to L. D. Faddeev.
Zero modes for the quantum Liouville model
The problem of definition of zero modes for quantum Liouville model is discussed and corresponding Hilbert space representation is constructed.
hep-th↗
3j-symbol for the modular double of SL_q(2,R) revisited
Modular double of quantum group SL_q(2,R) with |q|=1 has a series of selfadjoint irreducible representations parameterized by s. Ponsot and Teschner considered a decomposition of the tensor product of two representations into irreducibles. In our paper we give more detailed derivation and some new proofs.
math-ph↗
Volkov's Pentagon for the Modular Quantum Dilogarithm
The new form of pentagon equations suggested by Volkov for the $ q $-exponential on the basis of formal series is derived within the Hilbert space framework for the modular version of the quantum dilogarithm.
math.QA↗
Separation of scattering and selfaction revisited
The definition of scattering operator in Quantum Field Theory is critically reconsidered. The correct treatment of one-particle states is connected with separation of selfaction from interaction. The formalism of functional integral is used for the description of such a separation via introduction of the quantum equation of motion.
hep-th↗
3+1 decomposition in the new action for the Einstein Theory of Gravitation
The action of recently proposed formulation of Einstein Theory of Gravitation is written according to 3+1 decomposition of the space-time variables. The result coincides with known formulation of Dirac and Arnowitt-Deser-Misner.
gr-qc↗
New variables for the Einstein theory of gravitation
The set of 10 covariant vector fields is taken as basic variables to describe the gravitational field. Metric $ g_{μν} $ is a composite field. A possibility for the gravitational constant to be described as a condensate of additional scalar field is discussed.
hep-th↗
Mass in Quantum Yang-Mills Theory
Among seven problems, proposed for XXI century by Clay Mathematical Institute, there are two stemming from physics. One of them is called "Yang-Mills Existence and Mass Gap". The detailed statement of the problem, written by A. Jaffe and E. Witten, gives both motivation and exposition of related mathematical results, known until now. Having some experience in the matter, I decided to completement their text by my own personal comments aimed mostly to mathematical audience.
math-ph↗
New action for the Hilbert-Einstein equations
The Hilbert-Einstein equations are derived in the formalism employing the imbedding of the space-time into linear 10-dimensional space. An extra antisymmetric tensor field is needed for this task.
hep-th↗
Knots as possible excitations of the quantum Yang-Mills fields
A hypothetical picture of massive excitations of 4-dimensional Yang-Mills quantum field theory as closed knotted fat strings is described.
hep-th↗
Discrete series of representations for the modular double of U_q(sl(2,R))
Modular double of quantum group U_q (sl(2)) with deformation parameter q=e^{iπτ} is a natural object explicitly taking into account the duality τ-> 1/τ. The use of the modular double in CFT allows to consider the region 1<c<25 for the central charge of the Virasoro algebra when |τ|=1. In this paper a new discrete series of representations for the modular double of U_q (sl(2,R)) is found for such τ.
math.QA↗
Discrete evolution for the zero-modes of the Quantum Liouville Model
The dynamical system for the zero modes of the Liouville Model, which is separated from the full dynamics for the discrete shifts of time $ t \to t + π$, is investigated. The structure of the modular double in quantum case is introduced.
hep-th↗
Strongly Coupled Quantum Discrete Liouville Theory. II: Geometric Interpretation of the Evolution Operator
It is shown that the N-th power of the light-cone evolution operator of 2N-periodic quantum discrete Liouville model can be identified with the Dehn twist operator in quantum Teichmuller theory.
hep-th↗
Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
The quantum discrete Liouville model in the strongly coupled regime, 1<c<25, is formulated as a well defined quantum mechanical problem with unitary evolution operator. The theory is self-dual: there are two exponential fields related by Hermitean conjugation, satisfying two discrete quantum Liouville equations, and living in mutually commuting subalgebras of the quantum algebra of observables.
hep-th↗
From Yang-Mills Field to Solitons and back again
Lecture delivered at XXXVI Summer School on Subnuclear Physics at Erice in September 1998. It contains a brief reflection on the development of QFT in late sixties and a discussion of the role of solitons in realistic field theoretic models.
hep-th↗
Algebraic Quantization of Integrable Models in Discrete Space-time
Just like decent classical difference-difference systems define symplectic maps on suitable phase spaces, their counterparts with properly ordered noncommutative entries come as Heisenberg equations of motion for corresponding quantum discrete-discrete models. We observe how this idea applies to a difference-difference counterpart of the Liouville equation. We produce explicit forms of of its evolution operator for the two natural space-time coordinate systems. We discover that discrete-discrete models inherit crucial features of their continuous-time parents like locality and integrability while the new-found algebraic transparency promises a useful progress in some branches of Quantum Inverse Scattering Method.
hep-th↗
(T*B)_q, q-analogue of model space and CGC generating matrices
We study relations between the deformed cotangent bundle (T*B)_q for the Borel subgroup B of a given simple Lie group G, the quantum Lie algebra J_q associated with the corresponding quantum group G_q and the matrices generating Clebsch-Gordan coefficients (CGC) for J_q. We reveal the connection of these objects to quantum analogue of the model space M and q-tensor operators.
q-alg↗
Representation Theory of Lattice Current Algebras
Lattice current algebras were introduced as a regularization of the left- and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry $U_q(\sg)$. Their representation theory is studied in detail. In particular, we construct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra. It is shown that for an arbitrary number of lattice sites, the representation categories of the lattice current algebras agree with their continuum counterparts.
q-alg↗