Nonlocal transformations in Batalin-Vilkovisky theory

In summary, the conversation discusses the concept of "nonlocal transformations" in the BV formalism and its relation to gauge theories with an open algebra. It is claimed that by going to a different basis for the algebra, closure can be achieved, even leading to abelian gauge algebra. However, this comes at the cost of having nonlocal and non relativistic covariant infinitesimal transformations. The speaker is seeking clarification on how this relates to local and covariant gauge theories, such as non-Abelian Yang-Mills, and whether dropping locality and covariance would result in an abelian theory. They also ask for references to further understand these statements.
  • #1
gentsagree
96
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?"
 
  • #3
Could you please provide references to where you read these statements? Perhaps then it would be easier to help.
 

1. What is the Batalin-Vilkovisky theory?

The Batalin-Vilkovisky theory is a mathematical framework used in theoretical physics to study gauge theories, such as quantum field theory, that exhibit local symmetries. It was developed by Igor A. Batalin and George Vilkovisky in the late 1970s and early 1980s.

2. What are nonlocal transformations in Batalin-Vilkovisky theory?

Nonlocal transformations in Batalin-Vilkovisky theory refer to a type of transformation that preserves the structure of the theory, but does not necessarily preserve locality. In other words, the transformation may involve changes in distant parts of the system, rather than just its immediate neighborhood.

3. How do nonlocal transformations affect the Batalin-Vilkovisky action?

Nonlocal transformations can change the Batalin-Vilkovisky action, which is an important quantity in the theory. These transformations can modify the gauge-fixing term in the action, leading to a different set of equations of motion.

4. Can nonlocal transformations be used to simplify calculations in Batalin-Vilkovisky theory?

Yes, nonlocal transformations can be used to simplify calculations in Batalin-Vilkovisky theory. In some cases, a nonlocal transformation can reduce a complicated problem to a simpler one, making it easier to obtain solutions.

5. Are there any applications of nonlocal transformations in Batalin-Vilkovisky theory?

Nonlocal transformations have been used in various applications of Batalin-Vilkovisky theory, such as in studies of topological field theories and the quantization of gauge theories. They have also been applied in the study of anomalies and the renormalization of quantum field theories.

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