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Hey everyone,</div>
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We will be having another remote theory seminar by Wayne Polyzou (U Iowa) today at 1pm. Please join us in L102 or on Zoom
<a id="LPlnk243874" href="https://jlab-org.zoomgov.com/j/1615906048?pwd=Wewk1enaAxKPTdKik1oOE10Utbictq.1">
https://jlab-org.zoomgov.com/j/1615906048?pwd=Wewk1enaAxKPTdKik1oOE10Utbictq.1</a>.</div>
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Title: Wavelet representation of quantum field theories</div>
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Abstract: I will discuss the use of Daubechies wavelets in quantum</div>
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field theory. Daubechies wavelets are fractal-valued functions</div>
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constructed from the fixed point of a renormalization group equation</div>
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by translations and scale transformations. Related functions are used</div>
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for data compression in JPEG photo files, the FBI fingerprint</div>
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database, and in movie frames in the film industry. The wavelet basis</div>
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is a basis for the square integrable functions on the real line with</div>
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the property that there are an infinite number of basis functions with</div>
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support in any open interval. In spite of their fractal nature,</div>
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locally finite linear combinations can pointwise represent low-degree</div>
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polynomials. The wavelet representation gives a formally exact</div>
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representation of the field as an infinite sum of well-defined almost</div>
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local discrete operators. Ill-defined operator products that appear</div>
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in the Hamiltonian are replaced by infinite sums of well-defined</div>
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products of operators. The wavelet representation has natural volume</div>
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and resolution truncations. The renormalization group equation can be</div>
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used to reduce the evaluations of integrals involving fractal valued</div>
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functions to finite linear algebra. Truncations to different</div>
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resolutions are exactly related by a dyadic renormalization of</div>
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parameters in the Hamiltonian and a canonical transformation. I will</div>
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give an example using similarity renormalization transformation to</div>
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decouple scales in this representation. I will also illustrate the</div>
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use of the wavelet representation in the evaluation of real-time</div>
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evolution of fields, using a discrete representation of the path</div>
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integral as the expectation value of a complex probability over</div>
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cylinder sets of discrete paths.</div>
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<span style="background-color: rgb(255, 255, 255);">--</span></div>
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Joe Karpie</div>
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Pronouns: He/His/Him</div>
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Postdoctoral Fellow</div>
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Theoretical and Computational Physics Center</div>
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Jefferson Lab</div>
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