Lect21_Parity

# Lect21_Parity - Lecture 21: The Parity Operator Phy851 Fall...

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Lecture 21: The Parity Operator Phy851 Fall 2009

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Parity inversion Symmetry under parity inversion is known as mirror symmetry Formally, we say that f(x) is symmetric under parity inversion if f(-x) = f(x) We would say that f(x) is antisymmetric under parity inversion if f(-x)=-f(x) The universe is not symmetric under parity inversion (beta decay) – Unless there is mirror matter (and mirror photons) – Would interact only weakly with matter via gravity z y x z y x P a :
Parity Operator Let us define the parity operator via: Parity operator is Hermitian: Parity operator is it’s own inverse Thus it must be Unitary as well 1 2 = Π ) ( ) ( x x x x x x x x x x x x + = = Π + = = Π δ Π = Π x x x = Π = ΠΠ 1 Π = Π Π = Π x x = Π 1 Π = Π

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Properties of the Parity operator Parity acting to the left:
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## This note was uploaded on 12/21/2011 for the course PHY 851 taught by Professor Moore,m during the Fall '08 term at Michigan State University.

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Lect21_Parity - Lecture 21: The Parity Operator Phy851 Fall...

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