Nonlocal transformations in Batalin-Vilkovisky theory

  • Context: Graduate 
  • Thread starter Thread starter gentsagree
  • Start date Start date
  • Tags Tags
    Theory Transformations
Click For Summary
SUMMARY

The discussion focuses on the concept of "nonlocal transformations" within the Batalin-Vilkovisky (BV) formalism, particularly in the context of gauge theories with open algebras. It asserts that one can transition to a different algebra basis that achieves closure, potentially resulting in an abelian gauge algebra. However, this transformation necessitates that the infinitesimal transformations become nonlocal and non-relativistic covariant. The implications for local and covariant gauge theories, such as non-Abelian Yang-Mills and supergravity, are explored, emphasizing the relationship between locality, covariance, and the algebraic structure of these theories.

PREREQUISITES
  • Understanding of Batalin-Vilkovisky formalism
  • Familiarity with gauge theories and their algebraic structures
  • Knowledge of non-Abelian Yang-Mills theory
  • Concepts of locality and covariance in theoretical physics
NEXT STEPS
  • Research "Batalin-Vilkovisky formalism and nonlocal transformations"
  • Study "Gauge theories with open algebras and their implications"
  • Examine "Locality and covariance in non-Abelian Yang-Mills theory"
  • Explore "Closure of gauge algebras in supergravity theories"
USEFUL FOR

The discussion is beneficial for theoretical physicists, particularly those specializing in gauge theories, algebraic structures in quantum field theory, and researchers exploring the implications of nonlocal transformations in the Batalin-Vilkovisky framework.

gentsagree
Messages
93
Reaction score
1
Hi,

Can anyone clarify what precisely is meant by "nonlocal transformations" in the BV formalism?

Specifically, they claim that for any gauge theory with an open algebra, it is possible to go to a different basis for the algebra whereby one achieves closure (and even one where the gauge algebra is always abelian!). They claim this is at the price that the infinitesimal transformations (the usual stuff, where the transformation of the field is proportional to the algebra generators) be nonlocal and non relativistic covariant.

I guess I'm trying to understand how related this is to my beloved local and covariant gauge theories, say non-Abelian Yang-Mills. Can anyone elaborate on the statements that "if I drop locality and covariance for Yang-Mills theory, then the theory becomes abelian?" or "if I drop locality and covariance for supergravity, then the algebra can always be closed?"
 
Could you please provide references to where you read these statements? Perhaps then it would be easier to help.
 

Similar threads

Graduate What are some example Feynman diagrams in Yang-Mills theory?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is My Localized Yang-Mills Theory Solution Correct?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Classical Yang-Mills Force Law ?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Quantum Gravity: Renormalization vs. Effective Field Theory
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Uncovering the Combinatorial Origins of Yang-Mills Theory?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate What is Gauge Invariance in QFT?
  • · Replies 15 ·
Replies
15
Views
7K
Graduate Gauge transformation of Yang-Mills field strength
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Twistors and celestial holography
  • · Replies 21 ·
Replies
21
Views
6K
Graduate Structure of Matter in Quantum Field Theory
  • · Replies 75 ·
3
Replies
75
Views
10K
Undergrad Trying To Conceptualize Two Dimensions Of Time
  • · Replies 2 ·
Replies
2
Views
5K