# Parity

## Intuitive

If you take a mirror, and look at a left hand in the mirror, it looks light a right hand. Such a process, which turns something behaving like a left hand into something like a right hand, is called a parity transformation in particle physics. http://axelmaas.blogspot.de/2011/11/chiral-or-why-left-and-right-is-not.html

Acting with a parity transformation on a system simply means that we create a mirrored copy of it. Another name for a parity transformation is spatial inversions.

So parity symmetry means mirror symmetry.

## Concrete

Explicitly, the parity operator acting on four-vectors is given by

$$\label{eq:pardef3d} \Lambda_P = \begin{pmatrix} 1& 0 & 0 & 0 \\ 0&-1 & 0 & 0\\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix}$$

This matrix flips all spatial coordinates and keeps the time coordinate unchanged.

## Abstract

The motto in this section is: the higher the level of abstraction, the better.

## History

Before Lee andYang, every physicist believed it to be obvious beyondquestion that the forces of nature are reflection-invariant, so that themirror image of every natural event is itself an equally probable naturalevent.This assumed property of nature was called the law of parity con-servation, because of the equality or parity between the mirror imageand the actual event itself.

Physicists are familiar with four forces, the strong, the electromag-netic, the weak, and the gravitational force. The strong force bindstogether the protons and neutrons that make up the nucleus at thecenter of every atom.The electromagnetic force causes the electrons inatoms to orbit their nucleus and emit light.The weak force is respon-sible for “beta decay,” the radioactive disintegration of nuclei by elec-tron emission. Gravity, the oldest and most familiar force, governs themotions of falling apples, the earth and the moon, the planets, stars,and galaxies.

In the 1950s physicists knew that the strong and electromagneticforces conserved parity. They unquestionably assumed that the weakforce conserved parity, too. It seemed inconceivable that it shouldn’t.No one could imagine that looking at nature in a mirror might yield aworld that couldn’t exist.

Then, two strange new and unstable particles, the tau and the theta,were discovered in cosmic rays. In most respects the two particlesseemed almost identical; they had the same mass and electric charge, butthey decayed differently. What could make two almost indistinguishable particles decay into two different final states? That was the famous tau-theta puzzle of the 1950s.

In 1956 Lee and his collaborator Chen-Ning Yang pointed out thatthe two particles might in fact be one and the same particle, which then,subject to the weak force, decayed in two different ways, but that thiscould only happen if the weak force responsible for its decay was notreflection-invariant. It was a preposterous suggestion that Lee and Yangtook seriously and systematically. They analyzed all previous experi-ments that had studied the weak force in atoms and nuclei and foundthat, contrary to everyone’s unquestioned belief, no previous experi-ment had ever truly tested the assumed symmetry between an event andits reflection.With further study, Lee and Yang suggested specific exper-iments to check for parity violation in nuclear weak decays.

Most physicists were skeptical. How, they wondered, could any ofnature’s laws not be symmetric under reflection? But within a fewmonths, by early 1957, Madame Wu and her collaborators carried outthe experiment Lee andYang proposed, and showed that they were vin-dicated. Lee and Yang received their Nobel Prize that same year.

Lee andYang’s discovery that Nature was slightly asymmetric sparkeda revolution. Slowly but inexorably, further experiments in the 1950sand 1960s revealed further subtle asymmetries of the weak interaction.T. D. was at the center of these investigations.

From My Life As A Quant by Emanuel Derman

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