- #1

RicardoMP

- 49

- 2

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- A
- Thread starter RicardoMP
- Start date

In summary, the conversation discusses the vector and axialvector currents in a quantum field theory context, where the currents are defined as a product of gamma matrices and Dirac spinors. The vector current is represented by a 1x4 matrix, the axialvector current by a 4x1 matrix, and the product in the middle results in a 4x4 matrix, ultimately giving a single number. The discussion also touches on the use of operators in quantum field theory.

- #1

RicardoMP

- 49

- 2

Physics news on Phys.org

- #2

- 24,488

- 15,026

So what you multiply in the sense of matrix multiplication is a "row bi-spinor" ##\times## "##4 \times 4## matrix" ##\times## a "column bi-spinor", which gives a number.

Of course, in QFT the ##\psi## are operators, and thus also the ##j^{\mu}##'s become operators (transforming as a four-vector or an axial-four-vector operator, respectively).

Vector currents are associated with the conservation of a vector quantity, such as electric charge or momentum, while axial vector currents are associated with the conservation of a pseudovector quantity, such as angular momentum. In QFT, vector currents are represented by vector fields, while axial vector currents are represented by pseudovector fields.

In QFT, symmetries play a crucial role in understanding the behavior of particles and their interactions. Vector currents are associated with continuous symmetries, such as gauge symmetries, while axial vector currents are associated with discrete symmetries, such as parity or time reversal symmetries.

In the Standard Model, vector and axial vector currents play a central role in the description of the fundamental interactions between particles. The electromagnetic and weak interactions are described by vector currents, while the strong interaction is described by axial vector currents.

One of the challenges in QFT is dealing with infinities that arise in certain calculations. Vector and axial vector currents are important in the renormalization process, which involves adjusting parameters in the theory to account for these infinities and make meaningful predictions.

Yes, there are many experimental observations that support the existence of vector and axial vector currents. For example, the decay of a neutral pion into two photons is a clear manifestation of the axial vector current, while the decay of a muon into an electron and two neutrinos is a manifestation of the vector current.

- Replies
- 1

- Views
- 921

- Replies
- 16

- Views
- 3K

- Replies
- 5

- Views
- 997

- Replies
- 6

- Views
- 1K

- Replies
- 1

- Views
- 1K

- Replies
- 24

- Views
- 2K

- Replies
- 3

- Views
- 2K

- Replies
- 5

- Views
- 2K

- Replies
- 1

- Views
- 1K

- Replies
- 4

- Views
- 2K

Share: