Questions tagged [lattice-gauge-theory]
The study of (particle physics) gauge theories on a spacetime that has been discretized into a lattice.
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Different sectors of the Ising gauge theory
The Hamiltonian of Quantum 2D Ising gauge theory is given by:
$$ H=-\sum_p \prod_{i\in \square}\sigma^z_i -g \sum_{i\in \text{links}} \sigma^x_i$$
This $H$ is invariant under the local symmetries:
$$ ...
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Existence of Schwinger Functions for QCD?
It seems to me the 'naive' approach to proving the existence of Yang-Mills in a rigorous context (via Osterwalder-Schrader $\to$ Wightman axioms), would be:
Study gauge invariant lattice QCD ...
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What intuition led to J. Wang and X.G. Wen's lattice formulation of the 3450 chiral gauge theory?
In the paper cited below, Juven Wang and Xiao-Gang Wen give an example of a lattice model that reduces to a chiral $U(1)$ gauge theory at low energy. The low energy theory is called the $3450$ model. ...
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How to visualize the $U(1)$ instanton event in (2+1)D compact lattice gauge field?
In the continuum limit of (2+1)-dimensional compact $U(1)$ gauge field, the instantons are input by hand in terms of nonconservation of magnetic flux $\int b$:
\begin{eqnarray}
\int dxdy [b(x,y,t+\...
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How Is Are Parton Distribution Functions (PDFs) Determined In Practice And In Theory?
I have put my actual questions in bold normal font, and the rest of this question clarifies what I mean to be asking, especially in terms of the depth and kinds of information I am looking for. ...
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Can I do anything instructive by simulating QED on a lattice?
For learning something about the degrees of freedom and underlying path integral math, is it possible to do some kind of scalar QED or normal QED simulation on a lattice in the same way Lattice QCD is ...
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Wilson loops as representations of the Lorentz group
Wilson loops in lattice $4d$ Yang-Mills theory are used to build various glueball states of different spins when they are applied to the vacuum. The spin dependence of such states is related with the ...
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What is the connection between vertex/spin models and gauge theory?
In the usual formulation of lattice gauge theories, one considers gauge variables on the links of a lattice (often hypercubic) taking value in some representation of a gauge group, $U_{ij} \in G$. The ...
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Why doesn't Peierls substitution capture the Lorentz force?
It's well known that the classical Hamiltonian governing the dynamics of a charged particle in a static magnetic field is
$$ S_{cl}[x,\dot{x}] = \int_0^t dt' \frac{1}{2}m\dot{\vec{x}}^2 + e\vec{A}(x)\...
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Resource recommendation for Kogut-Susskind Hamiltonian formalism for lattice gauge theory
Recently, quantum simulations for quantum field theories have been a hot topic of research. In these calculations, the lattice calculations are done using the Hamiltonian formalism in contrast to the ...
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Lattice differentiation and Locality
Assume we define the locality of a theory in the following way:
Assume we have a theory of real scalars, so this theory is non local if the action has terms like
$$\int d^dx\,\phi(x)V(x-y)\phi(y).$$
...
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Instantons in the Global $O(2)$ Model (Compact scalar field) - Polyakov textbook
This question is related with Polyakov, "Gauge Fields and Strings" section 4.2
In section 4.2, partition function is
\begin{equation}
Z=\sum_{n_{x,\delta}}\int_{-\pi}^{\pi}\prod_x\frac{d\...
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Restoring Poincaré symmetries in Hamiltonian lattice field theories
I can imagine how the continuum limit of a non-relativistic quantum field theory discretized on a spatial lattice restores the Galilean symmetries of the original theory. But how does this work for ...
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Extracting a gauge-invariant variable from a given Wilson line? (NOT Wilson loop)
Let $W[x_i,x_f]$ be the Wilson line as defined here.
Under a local gauge transform $g(x)$, it transforms as
\begin{equation}
W[x_i,x_f] \to g(x_f)W[x_i,x_f] g^{-1}(x_i)
\end{equation}
which is shown ...
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Topological classification of (classical, Abelian) vortices on a lattice
Consider the XY model on the square lattice. A field configuration $\theta$ is specified by an element of the Abelian group $\mathbb{R}/2\pi \simeq U(1)$ at each vertex of the lattice. The gradient of ...
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