Renormalization: An Introduction (Theoretical and Mathematical Physics)

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The Foundation. Our Business Model. Organizations benefitting from our activities. Submissions Current status: Has been resubmitted. Submission Strengths 1- a new approach to variational states in field theory, elegant and simple 2- a possibly deep relation to topological properties of conformal field theory. Weaknesses 1- nothing serious, a few references should be added and a few extra comments made.

Report Inspired by previous work on quantum quenches and the entanglement spectrum, Cardy uses conformal field theory to make a variational ansatz for the ground state of a massive field theory. Strengths See report.

Weaknesses See report. Report The paper is devoted to the use of smeared boundary states of conformal field theory for approximating the ground state of massive field theories. Requested changes No changes requested.

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This observation may support the idea that a seemingly deterministic evolution is actually accompanied by an integration over some fluctuating degrees of freedom. The canonical form of the kinetic term is particularly important for our purpose to interpret the gradient flow as an RG flow see discussions around Eq. Note that the first two terms in Eq. The next three terms have a natural interpretation with Feynman diagrams see Fig.

In fact, the third term in Eq. The fifth term represents the contraction of propagators in a two-particle reducible diagram. A Feynman diagrammatic interpretation of Eq. By linearizing Eqs. In this paper, we have investigated the RG structure of the gradient flow. We wrote down the basic equation that determines the evolution of the action and considered an LPA to our equation, and showed that the result has a nice interpretation with Feynman diagrams. A careful treatment of the anomalous dimension will be given in a forthcoming paper. It is tempting to regard Eq.

However, one must be careful in establishing this relationship, because the RG interpretation of Eq. It thus should be interesting to write down an equation that incorporates the effect of the change of variable in a form of differential equation. We thus expect that the two expectation values 5. We leave the confirmation of this expectation for future work.

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Although the present paper only discusses scalar field theory, the extension to other field theories should be straightforward. The generalization to field theories in curved spacetime will also be interesting. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Sign In or Create an Account. Sign In.

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