Mathematical Quantum Field Theory - Free Quantum Fields - Comments

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The discussion focuses on the Schwinger-Dyson equation as a foundational aspect of Mathematical Quantum Field Theory, particularly in relation to free quantum fields. It highlights the equation's role as a precursor to the quantum master equation, which is crucial for understanding the absence of quantum anomalies during the renormalization of gauge theories. The implications of this relationship will be explored further in chapter 16 of the referenced material. The importance of these concepts in the broader context of quantum field theory is emphasized. Understanding these equations is essential for advancing in the field.
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Greg Bernhardt submitted a new PF Insights post

Mathematical Quantum Field Theory - Free Quantum Fields
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The Schwinger-Dyson equation at this point (prop. 14.27) may look innocent, but in chapter 16 we will see that it is already the free archetype of the important condition known as the "quantum master equation" or "master Ward identity" which controls the absence of quantum anomalies in renormalization of gauge theories.
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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