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This is not a question, let's list down all the effects resulting from breaking or preserving of various discrete symmetries, on various observables, be it in condensed matter or in high energy. Please discuss the subtleties, if there are any.

Some examples would be:

  1. The off-diagonal elements of conductivity are finite if T-symmetry is broken, otherwise it's zero.
  2. Breaking chiral symmetry gives rise to mass (apart from Higg's mechanism).
  3. Breaking inversion symmetry gives rise to Rashba (spin-orbit coupling) effect.
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Existence of an intrinsic electric dipole moment (EDM) for fundamental particles (or even for atoms and molecules) requires breaking parity and time reversal symmetry.

CP violating terms in the standard model are thought to give the electron and other particles tiny EDMs. BSM physics often predicts larger EDMs, and so EDM measurements can be very sensitive probes of new physics.

[See "CP violation without strangeness : electric dipole moments of particles, atoms, and molecules" by Iosif B. Khriplovich & Steve K. Lamoreaux.]

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