Integral Transforms in Relativistic Quantum Constraint Mechanics
2011
In relativistic quantum constraint mechanics the state of a physical system is constrained to a 3-dimensional subspace of Minkowski 4-space. Fourier transformation can be used to relate this state between constraint spaces in 4-position and 4-momentum space. It is shown that integral transforms of this nature can be carried out using Lorentz-invariant 3dimensional constraint space coordinates such that a complete equivalence class of 4-space representations can be constructed from the transform. This method is further applied to develop a relativistic generalization of the Segal-Bargmann transformation that leads to the representation of quantum systems in a three-dimensional subspace of Bargmann 4-space.
Keywords:
- Mechanics
- Center of mass (relativistic)
- Quantum phase estimation algorithm
- Discrete mathematics
- Quantum mechanics
- Four-vector
- Relativistic quantum mechanics
- Quantum operation
- Mathematics
- Quantum statistical mechanics
- Linear canonical transformation
- Mathematical analysis
- Symmetry in quantum mechanics
- Quantum process
- Correction
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- Cite
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