# What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT?

What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT? The question is motivated by this preprint arXiv:1203.0609 by Murayama and Watanabe.

Also, what is the basic difference between

• a theory that is non-relativistic approximation to relativistic theory, and

• a fundamentally Lorentz non-invariant theory?

-

Lorentz invariant theories are desirable because their behaviour does not depend on a specific frame of reference.

A theory non-relativistic approximation to a relativistic theory can usually be acquired by expanding physical quantities which are part of a relativistic around low velocities or momenta. A fundamentally Lorentz non-invariant theory is just some theory which does not possess the property of Lorentz-invariance.

-