Related papers: Lie fields revisited
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
A covariant description of the canonical theory for interacting classical fields is developed on a space-like hypersurface. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in…
We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also space-time points, are raised to the status of matrices [equivalently operators]. These matrices obey a…
A displacement operator d_\zeta is introduced, verifying commutation relations [d_\zeta, a_f^\dagger]=[d_\zeta, a_f]=\zeta(f)d_\zeta with field creation and annihilation operators that verify [a_f,a_g]=0, [a_f,a_g^\dagger]=(g,f), as usual.…
Following up the work of [1] on deformed algebras, we present a class of Poincar\'e invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation…
Starting from the instant form of relativistic quantum dynamics for a system of interacting fields, where amongst the ten generators of the Poincare group only the Hamiltonian and the boost operators carry interactions, we offer an…
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian…
In this paper we develop a systematic quantum field theory based approach to the vacuum replica recently found to exist in effective low energy models in hadronic physics. A local operator creating the replica state is constructed…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
The features of vacuum particle creation in an external classical field are studied for simplest external field models in $3 + 1$ dimensional QED. The investigation is based on a kinetic equation that is a nonperturbative consequence of the…
Background: The vacuum in the light-front representation of quantum field theory is trivial while vacuum in the equivalent canonical representation of the same theory is non-trivial. Purpose: Understand the relation between the vacuum in…
Let us consider a Lie (super)algebra $G$ spanned by $T_{\alpha}$ where $T_{\alpha}$ are quantum observables in BV-formalism. It is proved that for every tensor $c^{\alpha_1...\alpha_k}$ that determines a homology class of the Lie algebra…
Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give…
We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension.…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
In Newtonian mechanics, inertial pseudoforces - or fictitious forces - appear in systems studied in non-Galilean reference frames; e.g., a centrifugal force seems to arise if the dynamics is analyzed in a rotating reference frame. The…
When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…
For any massless, irreducible representation of the covering of the proper, orthochronous Poincar\'e group we construct covariant, free quantum fields that generate the representation space from the vacuum and are localized in semi-infinite…