CPT Invariance of Hermitian & Lorentz Lagrangians

Apr 27, 2015

Breo

Are all the hermitian and lorentz invariant lagrangians, invariant under the combination of CPT?

If yes, how can it be proved?

Apr 27, 2015

ChrisVer

Gold Member

http://users.ox.ac.uk/~mert2255/papers/cpt.pdf

Here is a rigorous proof of the CPT-theorem...
In a general framework, Lorentz invariance is not needed for CPT symmetry to exist. Neither the violation of CPT would necessarily mean the violation of Lorentz invariance.

1. What is CPT invariance and why is it important in physics?

CPT invariance is a fundamental concept in physics that states that the laws of physics should remain unchanged under the combined operations of charge conjugation (C), parity inversion (P), and time reversal (T). This means that if we reverse the direction of time, switch particles with their antiparticles, and mirror the universe, the laws of physics should still hold true. It is important because it allows us to make predictions and understand the behavior of particles and systems in the universe.

2. What is a Hermitian Lagrangian and how does it relate to CPT invariance?

A Hermitian Lagrangian is a mathematical function used in quantum field theory to describe the dynamics of particles and their interactions. It is called Hermitian because it satisfies a mathematical property known as Hermiticity. This property is important for maintaining CPT invariance, as it ensures that the Lagrangian remains unchanged under the combined CPT transformation.

3. What is a Lorentz Lagrangian and how does it relate to CPT invariance?

A Lorentz Lagrangian is a type of Lagrangian that is invariant under Lorentz transformations, which describe how the laws of physics should appear the same to all observers moving at constant velocities. This is important for maintaining CPT invariance because it ensures that the laws of physics hold true regardless of the reference frame in which they are observed.

4. How do we test for CPT invariance experimentally?

One of the most common ways to test for CPT invariance experimentally is by studying the properties of particles and their antiparticles. If CPT invariance is violated, it would result in differences in the properties of particles and antiparticles. Another way is through precision measurements of symmetries in physical systems, such as the decay rates of particles.

5. What are the implications of a violation of CPT invariance?

If CPT invariance is found to be violated, it would have significant implications for our understanding of the laws of physics and the universe. It would suggest that there are fundamental symmetries that are not preserved in nature, which could lead to the development of new theories and models to explain these discrepancies. It could also have implications for our understanding of the origin of the universe and the nature of matter and antimatter.