The Bianchi Identity for p-Form Fields: Understanding Its Significance

[Moataz]

Dear All
Does anyone have an online (preferably) source on the Bianchi identity
on p-form fields (dF=0)? I would like to read more on the various
cases, particularly the physical meaning of a violated Bianchi
identity.
Thanks ...

 

[klw1026]

Dear Moataz,

I think the best place for this is the book "Gauge Fields, Knots and Gravity" by John Baez.

 

[sir-pinski]

Hi there,

The Bianchi identity is a fundamental concept in differential geometry and is used to study the behavior of p-form fields. It states that the exterior derivative of a p-form field is always zero, meaning that the field is closed. This identity is significant because it allows us to understand the behavior of these fields and make predictions about their behavior.

There are many online sources that discuss the Bianchi identity for p-form fields. One good source is the Stanford Encyclopedia of Philosophy, which has a detailed entry on differential forms and the Bianchi identity. Another good source is the MathWorld website, which has a section specifically dedicated to the Bianchi identity and its applications.

In terms of understanding the physical meaning of a violated Bianchi identity, this can vary depending on the specific field and situation. In general, a violated Bianchi identity can indicate the presence of sources or sinks in the field, or it can suggest that the field is not closed and may be subject to external influences. Further analysis and calculations are often needed to fully understand the implications of a violated Bianchi identity.

I hope this helps and provides some useful resources for your research. Best of luck!