相关论文: $\phi^4$ Field theory on a Lie group
We discuss a D-dimensional Euclidean scalar field interacting with a scale invariant quantized metric. We assume that the metric depends on d-dimensional coordinates where d<D. We show that the interacting quantum fields have more regular…
The paper is devoted to the problem of finding free generators in the fields of invariants for actions of unipotent groups on affine varieties. We consider the case when the unipotent group is the unipotent radical in an arbitrary parabolic…
Extending the principle of local gauge invariance $\psi(x)\to \exp\left(\imath \sum_A \omega^A(x)T^A \right) \psi(x), x \in \mathbb{R}^d$, with $T^A$ being the generators of the gauge group $\mathcal{A}$, to the fields $\psi(g)\equiv…
We consider a family of $\kappa$-Poincar\'e invariant scalar field theories on 4-d $\kappa$-Minkowski space with quartic orientable interaction, that is for which $\phi$ and its conjugate $\phi^\dag$ alternate in the quartic interaction,…
The free propagator for the scalar $\lambda \phi^4$--theory is calculated exactly up to the second derivative of a background field. Using this propagator I compute the one--loop effective action, which then contains all powers of the field…
Let $F$ be a local non archimedian field of characteristic $0$, and $G$ a non-connected reductive group over $F$. We denote $G^0$ the connected component of the identity and assume the quotient $G/G^0$ is abelian. For $f$ a locally constant…
Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_k (x_1, x_2) of dimension (k,k). For a {\it globally conformal invariant} (GCI) theory we write down…
Metric independent $\sigma$ models are constructed. These are field theories which generalise the membrane idea to situations where the target space has fewer dimensions than the base manifold. Instead of reparametrisation invariance of the…
We construct the moduli spaces associated to the solutions of equations of motion (modulo gauge transformations) of the Poisson sigma model with target being an integrable Poisson manifold. The construction can be easily extended to a case…
We use algebraic geometry to study the anomaly-free representations of an arbitrary gauge Lie algebra for 4-dimensional spacetime fermions. For irreducible representations, the problem reduces to studying the Lie algebras $\mathfrak{su}_n$…
The gauge field strength tensor $F_{\mu \nu}$ in Abelian and non-Abelian local gauge field theories is a key object in the construction of the Lagrangian since it provides the kinetic term(s) of the gauge field(s) $A_\mu$. When introducing…
Our main proposition is that field equations for all spins can be obtained from Casimir eigenvalue equations for Poincare group. We have already confirm that statement for massive scalar, spinor and vector fields in Ref.[1]. In the present…
Let \phi be an endomorphism of a finitely generated free group F, and let H be a finite-index subgroup of F that is invariant under \phi. The nonzero eigenvalues of \phi are contained in the eigenvalues of \phi restricted to H.
In this work we use generalized deformed gauge groups for investigation of symmetry of general relativity (GR). GR is formulated in generalized reference frames, which are represented by (anholonomic in general case) affine frame fields.…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
It is pointed out that one-component \phi^4 lattice theory in four dimensions has a non-perturbative sector which can be studied by means of an exact duality transformation of its Ising limit. This duality maps it to a membrane model. As a…
For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra $A$ of functions and the Lie algebra $\mathcal{V}$ of vector fields on the variety. We prove that a gauge…
The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of…
The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. Scale invariance is considered in the context of a gravitational theory where the action, in the first order formalism, is of the form $S…
We extend the Gelfand and Graev construction of generalized Fourier transforms on basic affine space from split groups to quasi-split groups over a local non-archimedean field $F$.