相关论文: A formalism for the renormalization procedure

Let $M$ be a compact oriented $d$-dimensional smooth manifold and $X$ a topological space. Chas and Sullivan \cite{Chas-Sullivan:stringtop} have defined a structure of Batalin-Vilkovisky algebra on $\mathbb{H}_*(LM):=H_{*+d}(LM)$. Getzler…

We prove that the differential graded Lie algebra of functionals associated to the Chern-Simons theory of a semisimple Lie algebra is homotopy abelian. For a general field theory, we show that the variational complex in the…

We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which…

First, we give a functorial construction of a group associated to a symmetric operad. Applied to the endomorphism operad it gives the group of formal diffeomorphisms. Second, we associate a symmetric operad to any family of decorated graphs…

We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann-Hilbert problem. Given a loop $\gamma(z), | z |=1$ of elements…

We introduce the concept of a holomorphic field theory on any complex manifold in the language of the Batalin-Vilkovisky formalism. When the complex dimension is one, this setting agrees with that of chiral conformal field theory. Our main…

The algebraic method of renormalization is applied to the standard model of electroweak interactions. We present the most important modifications compared to theories with simple groups.

We discuss the notion of a Batalin-Vilkovisky (BV) algebra and give several classical examples from differential geometry and Lie theory. We introduce the notion of a quantum operator algebra (QOA) as a generalization of a classical…

We describe a procedure, called regularisation, that allows us to study geometric structures on Lie algebroids via foliated geometric structures on a manifold of higher dimension. This procedure applies to various classes of Lie algebroids;…

The Batalin-Vilkovisky master equations, both classical and quantum, are precisely the integrability equations for deformations of algebras and differential algebras respectively. This is not a coincidence; the Batalin-Vilkovisky approach…

In this article, we define a doubling procedure for the bialgebra of specified Feynman graphs introduced in a previous paper \cite {DMB}. This is the vector space generated by the pairs $(\bar \Gamma, \bar \gamma)$ where $\bar \Gamma$ is a…

We study a certain class of bulk-boundary systems in the Batalin-Vilkovisky (BV) formalism. We construct factorization algebras of observables for such bulk-boundary systems, and show that these factorization algebras have a natural Poisson…

In a previous paper "Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces" (arXiv:0903.0187) we presented a new method for renormalization in Euclidean configuration spaces based on certain renormalization maps. This…

An invariant definition of the operator $\Delta $ of the Batalin-Vilkovisky formalism is proposed. It is defined as the divergence of a Hamiltonian vector field with an odd Poisson bracket (antibracket). Its main properties, which follow…

We develop the Batalin-Vilkovisky formalism for classical field theory on generic globally hyperbolic spacetimes. A crucial aspect of our treatment is the incorporation of the principle of local covariance which amounts to formulate the…

We show that the Kaehler structure can be naturally incorporated in the Batalin-Vilkovisky formalism. The phase space of the BV formalism becomes a fermionic Kaehler manifold. By introducing an isometry we explicitly construct the fermionic…

We consider semidensities on a supermanifold E with an odd symplectic structure. We define a new $\Delta$-operator action on semidensities as the proper framework for Batalin-Vilkovisky formalism. We establish relations between…

We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a…

Starting from a solution to the classical Batalin-Vilkovisky master equation,an extended solution to an extended master equation is constructed by coupling all the observables, the anomaly candidates and the generators of global symmetries.…

A new operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real space Renormalization Group is introduced, in which cell-overlapping is the key concept.…