Related Experiment Video
Updated: Apr 27, 2026
06:26
Stereo-Imaging System DLT Calibration to Capture 3D In Situ Displacements of Stretched Peripheral Nerves
Published on: January 12, 2024
887
From scale invariance to Lorentz symmetry.
1Theory Group, Physics Department, CERN, CH-1211 Geneva 23, Switzerland; FSB/ITP/LPPC, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland; and Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312 Moscow, Russia.
Physical Review Letters
|July 5, 2014
Summary
A unitary field theory in 1+1 dimensions with scale invariance exhibits infinite dimensional conformal algebra symmetry. This symmetry implies the presence of Lorentz groups acting on the theory's operator algebra.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
Background:
- Exploring symmetries in quantum field theories is crucial for understanding their properties.
- Conformal algebra plays a significant role in various areas of physics, including critical phenomena and string theory.
Purpose of the Study:
- To investigate the symmetries of a unitary, translationally invariant field theory in 1+1 dimensions.
- To determine if scale invariance implies higher symmetries under specific conditions.
Main Methods:
- Analysis of a unitary field theory in 1+1 dimensions.
- Application of isotropic scale invariance and standard assumptions on spectrum and causality.
- Investigation of operator algebra and signal propagation.
Main Results:
- The theory possesses an infinite dimensional symmetry.
- This symmetry is identified as one or several copies of the conformal algebra.
- The presence of Lorentz groups acting on the operator algebra is implied.
Conclusions:
- Unitary, scale-invariant field theories in 1+1 dimensions inherently possess conformal symmetry.
- The conformal symmetry leads to the emergence of Lorentz groups within the operator algebra, offering insights into the structure of such theories.
Related Concept Videos
01:27Gauss's Law: Planar Symmetry
7.5K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
7.5K
01:20Gauss's Law: Cylindrical Symmetry
7.3K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
7.3K
01:28Symmetry in Maxwell's Equations
2.9K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
2.9K
01:26Scaling
712
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
712
01:26Gauss's Law: Spherical Symmetry
7.2K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has...
7.2K
01:21Properties of Fourier series II
801
Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...
A function f(t) is...
801