Wavelets in field theory

Bulut, Fatih; Polyzou, W. N.

doi:10.1103/physrevd.87.116011

Cited by 32 publications

(51 citation statements)

References 19 publications

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“…reduced to finite linear algebra) using (2-3) and the scaling equation (1). This is discussed in detail in [11] and the appendix. See also [27][28][23] [24] for general methods to compute integrals involving wavelets and scaling functions.…”

Section: Wavelet Discretized Fieldsmentioning

confidence: 99%

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Multiresolution decomposition of quantum field theories using wavelet bases

2017

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We investigate both the theoretical and computational aspects of using wavelet bases to perform an exact decomposition of a local field theory by spatial resolution. The decomposition admits natural volume and resolution truncations. We demonstrate that flow equation methods can be used to eliminate short-distance degrees of freedom in truncated theories. The method is tested on a free scalar field in one dimension, where the spatial derivatives couple the degrees of freedom on different scales, although the method is applicable to more complex field theories. The flow equation method is shown to decouple both distance and energy scales in this example. The response to changing the volume and resolution cutoffs and the mass is discussed.

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Section: Wavelet Discretized Fieldsmentioning

confidence: 99%

“…The weights g l in equation (11) are related to the weights h l used in (1) except the signs alternate and the order of the indices is reversed.…”

Section: Background -Wavelet Basismentioning

confidence: 99%

Multiresolution decomposition of quantum field theories using wavelet bases

2017

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“…To be concluded, we have wavelet transform is used to construct divergence free Green functions [2,20,21].…”

Section: Discussionmentioning

confidence: 99%

On Quantization in Light-cone Variables Compatible with Wavelet Transform

Altaisky

Kaputkina

2016

Int J Theor Phys

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Canonical quantization of quantum field theory models is inherently related to the Lorentz invariant partition of classical fields into the positive and the negative frequency parts u(x) = u + (x) + u − (x), performed with the help of Fourier transform in Minkowski space. That is the commutation relations are being established between non localized solutions of field equations. At the same time the construction of divergence free physical theory requires the separation of the contributions of different space-time scales. In present paper, using the light-cone variables, we propose a quantization procedure which is compatible with separation of scales using continuous wavelet transform, as described in our previous paper [1].

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“…are constant coefficients. They can be computed exactly using the renormalization group equation and properties of the basis [5] [3] .…”

Section: Multiresolution Decomposition Of Quantum Fieldsmentioning

confidence: 99%

“…The resulting truncated Hamiltonian has a finite number of degrees of freedom. The scaling properties of the integrals [3], (5), lead to an exact renormalization group equation for infinite volume truncated Hamiltonians with different resolutions…”

Section: Truncated Quantum Fieldsmentioning

confidence: 99%

Multi-scale Methods in Quantum Field Theory

2018

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Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is finite. The wavelet decomposition has natural resolution and volume truncations that can be used to isolate the relevant degrees of freedom. The application of flow equation methods to construct effective theories that decouple coarse and fine scale degrees of freedom is examined.PACS numbers:

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Wavelets in field theory

Cited by 32 publications

References 19 publications

Multiresolution decomposition of quantum field theories using wavelet bases

Multiresolution decomposition of quantum field theories using wavelet bases

On Quantization in Light-cone Variables Compatible with Wavelet Transform

Multi-scale Methods in Quantum Field Theory

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