By Arthur S. Wightman

Cargèse Lectures in Theoretical Physics

**Read or Download [Chapter] Introduction to Some Aspects of the Relativistic Dynamics of Quantized Fields PDF**

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**Extra info for [Chapter] Introduction to Some Aspects of the Relativistic Dynamics of Quantized Fields**

**Example text**

0 for all p and q . 60) where again both signs of p 0 are allowed. The usual transformation law U(a, A ) tf;(x ) U (a, A )- 1 S(A- 1 ) tf;(A(A ) x + a) for a spinor field is valid for this if;. '0 in contrast to the situation in a theory satisfying the spectral condition. Bilinear quantities such as = J d 2 xf(x) tf;+(x) iy/J. tf;(x) make sense without Wick ordering in this non-physical world, as one easily sees from their definition in

12 x ) ( l + ;2 i. {y + n m-V2-x2}) = = -4 l (4. 10) so the two-point distribution has a singularity like RELATIVISTIC DYNAMICS OF QUANTIZED FIELDS 201 on the light cone x2 = 0. 1 1 ) oo (This is what is usually meant by the statement that the field strength renormalization is infinite. ) The proof is simply that integrals of the form J dp(a)H&1>(vamz) 00 0 J dp(a) = 0 as does H&1>(vmz). with 00 < 0 oo will have the same singularity at z To see how solutions of coupled field equations can be constructed from this exponential, consider the two-component field.

Pn ) � ( - l )i+1 J dQ0(q)f( - (p� - q)) u+ ( pj) iy/J. u(q) x i I x p