GRADED DIFFERENTIAL ALGEBRAS—ALGEBRAIC STRUCTURE OF THE BRST SYMMETRY

2020 ◽  
pp. 165-186
Keyword(s):  
Algebraic Structure ◽  
Brst Symmetry ◽  
Differential Algebras

Algebraic structure of the BRST symmetry

1994 ◽  
Vol 35 (11) ◽  
pp. 5862-5868
Author(s):  
Liviu Tǎtar ◽  
Radu Tǎtar
Keyword(s):  
Algebraic Structure ◽  
Brst Symmetry

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

Gauge Field Theory in Natural Geometric Language

2020 ◽  
Author(s):  
Daniel Canarutto
Keyword(s):  
Particle Physics ◽  
Quantum Physics ◽  
Brst Symmetry ◽  
Natural Extension ◽  
Integrated Approach ◽  
Arbitrary Spin ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Standard View ◽  
Spinor Bundle

This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connection and by a soldering form (a ‘tetrad’) valued in a vector bundle naturally constructed from the assumed 2-spinor bundle. We give a presentation of electroweak theory that dispenses with group-related notions, and we introduce a non-standard, natural extension of it. Also within the 2-spinor approach we present: a non-standard view of gauge freedom; a first-order Lagrangian theory of fields with arbitrary spin; an original treatment of Lie derivatives of spinors and spinor connections. Furthermore we introduce an original formulation of Lagrangian field theories based on covariant differentials, which works in the classical and quantum field theories alike and simplifies calculations. We offer a precise mathematical approach to quantum bundles and quantum fields, including ghosts, BRST symmetry and anti-fields, treating the geometry of quantum bundles and their jet prolongations in terms Frölicher's notion of smoothness. We propose an approach to quantum particle physics based on the notion of detector, and illustrate the basic scattering computations in that context.

scholarly journals Gauged double field theory as an L∞ algebra

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Eric Lescano ◽  
Martín Mayo
Keyword(s):  
Field Theory ◽  
Algebraic Structure ◽  
Classical Field ◽  
Field Theories ◽  
Lie Derivative ◽  
Linear Perturbation ◽  
Double Field Theory ◽  
Generalized Frame ◽  
Symmetry Transformations ◽  
Classical Field Theories

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

scholarly journals Polymorphic Iterable Sequential Effect Systems

2021 ◽  
Vol 43 (1) ◽  
pp. 1-79
Author(s):  
Colin S. Gordon
Keyword(s):  
Algebraic Structure ◽  
Position Effect ◽  
Type Systems ◽  
Sequential Effect ◽  
Prior Work ◽  
Sequential Effects ◽  
Wide Range ◽  
The Relationship ◽  
Categorical Semantics

Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden. But our general understanding of effect systems is limited primarily to systems where the order of effects is irrelevant. Understanding such systems in terms of a semilattice of effects grounds understanding of the essential issues and provides guidance when designing new effect systems. By contrast, sequential effect systems—where the order of effects is important—lack an established algebraic structure on effects. We present an abstract polymorphic effect system parameterized by an effect quantale—an algebraic structure with well-defined properties that can model the effects of a range of existing sequential effect systems. We define effect quantales, derive useful properties, and show how they cleanly model a variety of known sequential effect systems. We show that for most effect quantales, there is an induced notion of iterating a sequential effect; that for systems we consider the derived iteration agrees with the manually designed iteration operators in prior work; and that this induced notion of iteration is as precise as possible when defined. We also position effect quantales with respect to work on categorical semantics for sequential effect systems, clarifying the distinctions between these systems and our own in the course of giving a thorough survey of these frameworks. Our derived iteration construct should generalize to these semantic structures, addressing limitations of that work. Finally, we consider the relationship between sequential effects and Kleene Algebras, where the latter may be used as instances of the former.

On A Multiplicativity up to Homotopy of the Gugenheim Map

2002 ◽  
Vol 9 (3) ◽  
pp. 549-566
Author(s):  
Z. Kharebava
Keyword(s):  
Cochain Complex ◽  
Differential Algebras ◽  
Graded Coalgebra

Abstract In the category of differential algebras with strong homotopy there is a Gugenheim's map {ρ 𝑖} : 𝐴* → 𝐶* from Sullivan's commutative cochain complex to the singular cochain complex of a space, which induces a differential graded coalgebra map of appropriate Bar constructions. Both (𝐵𝐴*, dBA , Δ,) and (𝐵𝐶*, dBC* , Δ,) carry multiplications. We show that the Gugenheim's map 𝐵{ρ 𝑖} : (𝐵𝐴*, dBA* , Δ,) → (𝐵𝐶*, dBC* , Δ,) is multiplicative up to homotopy with respect to these structures.

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