[Theory-seminars] Theory Seminar Today

[Joseph Karpie]

Hey everyone,

We will be having another remote theory seminar by Wayne Polyzou (U Iowa) today at 1pm. Please join us in L102 or on Zoom https://jlab-org.zoomgov.com/j/1615906048?pwd=Wewk1enaAxKPTdKik1oOE10Utbictq.1.

Title: Wavelet representation of quantum field theories

Abstract: I will discuss the use of Daubechies wavelets in quantum
field theory.  Daubechies wavelets are fractal-valued functions
constructed from the fixed point of a renormalization group equation
by translations and scale transformations.  Related functions are used
for data compression in JPEG photo files, the FBI fingerprint
database, and in movie frames in the film industry.  The wavelet basis
is a basis for the square integrable functions on the real line with
the property that there are an infinite number of basis functions with
support in any open interval.  In spite of their fractal nature,
locally finite linear combinations can pointwise represent low-degree
polynomials.  The wavelet representation gives a formally exact
representation of the field as an infinite sum of well-defined almost
local discrete operators.  Ill-defined operator products that appear
in the Hamiltonian are replaced by infinite sums of well-defined
products of operators.  The wavelet representation has natural volume
and resolution truncations.  The renormalization group equation can be
used to reduce the evaluations of integrals involving fractal valued
functions to finite linear algebra.  Truncations to different
resolutions are exactly related by a dyadic renormalization of
parameters in the Hamiltonian and a canonical transformation.  I will
give an example using similarity renormalization transformation to
decouple scales in this representation.  I will also illustrate the
use of the wavelet representation in the evaluation of real-time
evolution of fields, using a discrete representation of the path
integral as the expectation value of a complex probability over
cylinder sets of discrete paths.


--
Joe Karpie
Pronouns: He/His/Him
Postdoctoral Fellow
Theoretical and Computational Physics Center
Jefferson Lab

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