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In several textbooks of QM I have read that Lorentz invariance is manifest in Heisnberg picture. How can we deduce that?
The Heisenberg picture is a formulation of quantum mechanics that describes the time evolution of a quantum system. It differs from the more commonly known Schrödinger picture in that the operators representing physical quantities are time-dependent, while the state vectors are time-independent.
The Heisenberg picture is based on the principles of special relativity, which includes Lorentz invariance. This means that the equations describing the time evolution of quantum systems in the Heisenberg picture are invariant under Lorentz transformations, which are transformations between different inertial reference frames.
Lorentz invariance is a fundamental principle of special relativity that states that the laws of physics should be the same for all inertial observers, regardless of their relative motion. This includes the laws of quantum mechanics, which are described by the Heisenberg picture.
Lorentz invariance is important in quantum mechanics because it ensures that the laws of physics are consistent across different reference frames. This is crucial for understanding the behavior of quantum systems, which can exhibit strange and counterintuitive phenomena.
The Heisenberg picture is one of several formulations of quantum mechanics, including the Schrödinger picture and the Dirac picture. Each of these formulations provides a different perspective on quantum mechanics, but they are all equivalent and can be used to describe the same physical systems.