Related Experiment Video
Updated: Jun 5, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Applying the variational principle to (1+1)-dimensional quantum field theories
Jutho Haegeman1, J Ignacio Cirac, Tobias J Osborne
1Ghent University, Department of Physics and Astronomy, Krijgslaan 281-S9, B-9000 Ghent, Belgium.
Physical Review Letters
|January 15, 2011
Summary
We introduce a new method for studying relativistic quantum field theories using continuous matrix product states. This approach overcomes challenges in applying variational methods and offers a novel regularization technique, avoiding fermion doubling and sign problems.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
Background:
- Variational methods in quantum field theory face challenges, particularly in relativistic settings.
- Existing methods can suffer from issues like fermion doubling and sign problems.
Purpose of the Study:
- To extend the continuous matrix product state (MPS) variational class to (1+1)-dimensional relativistic quantum field theories.
- To develop a fermionic MPS approach that avoids fermion doubling and sign problems.
- To provide a new regularization technique for quantum field theories.
Main Methods:
- Extension of the continuous matrix product state (MPS) variational class.
- Introduction of a fermionic version of the continuous MPS.
- Application to (1+1)-dimensional relativistic quantum field theories.
Main Results:
- Overcoming Feynman's difficulties with variational procedures in relativistic theories.
- Development of a fermionic MPS formulation free of fermion doubling and sign problems.
- Successful study of momentum occupation for free massive Dirac fermions.
- Analysis of chiral symmetry breaking in the Gross-Neveu model.
Conclusions:
- The continuous matrix product state formalism offers a powerful new tool for relativistic quantum field theories.
- This method provides an effective way to regularize quantum field theories.
- The fermionic implementation successfully addresses long-standing issues in quantum field theory calculations.
Related Concept Videos
01:17The Principle of Superposition and the Gravitational Field
The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...
01:17Differential Form of Maxwell's Equations
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
01:10First Law: Particles in One-dimensional Equilibrium
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...
02:45The Quantum-Mechanical Model of an Atom
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
01:24Calculation of First-Law Quantities II
The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...
01:13Force and Potential Energy in One Dimension
Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...