# Hamilton-Jacobi analysis of the four dimensional BF model with cosmological term

## TL;DR

This paper applies Hamilton-Jacobi analysis to a four-dimensional BF model with a cosmological term, deriving the complete set of involutive Hamiltonians, gauge generators, and the reduced phase space to understand its integrability and symmetries.

## Contribution

It provides a comprehensive Hamilton-Jacobi constraint analysis of the 4D BF model with cosmological term, identifying involutive Hamiltonians and gauge generators.

## Key findings

- Complete set of involutive Hamiltonians obtained
- Reduced phase space identified
- Equations of motion and gauge generators derived

## Abstract

In this work we perform the Hamilton-Jacobi constraint analysis of the four dimensional Background Field (BF) model with cosmological term. We obtain the complete set of involutive Hamiltonians that guarantee the integrability of the system and identify the reduced phase space. From the fundamental differential we recover the equations of motion and obtain the generators of the gauge and shift transformations.