Related Experiment Video
Updated: Sep 7, 2025
06:55
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
8.0K
On Globalized Traces for the Poisson Sigma Model
1Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland.
Communications in Mathematical Physics
|June 21, 2022
Summary
A new global trace formula for the Poisson Sigma Model on a disk is introduced using the Batalin-Vilkovisky formalism. This framework incorporates zero modes and connects to existing theories in topological quantum mechanics.
Area of Science:
- Theoretical Physics
- Mathematical Physics
Background:
- The Poisson Sigma Model (PSM) is a key framework in theoretical physics, particularly in understanding topological field theories.
- Trace formulas are essential tools for analyzing quantum field theories, relating mathematical structures to physical properties.
Purpose of the Study:
- To present a globalized trace formula for the Poisson Sigma Model on a disk.
- To incorporate the concept of zero modes into this global construction.
- To establish connections with existing results in topological quantum mechanics and related theorems.
Main Methods:
- Utilizing the Batalin-Vilkovisky (BV) formalism for a formal global picture.
- Developing a global construction for the trace formula.
- Analyzing the symplectic case of the PSM with a cotangent target.
Main Results:
- A globalized trace formula for the Poisson Sigma Model on the disk is successfully presented.
- The construction explicitly includes the treatment of zero modes.
- For the symplectic case, the formula reduces to a known construction in 1-dimensional Chern-Simons theory.
Conclusions:
- The presented global trace formula offers a unified approach to the Poisson Sigma Model on a disk.
- The work highlights the utility of the Batalin-Vilkovisky formalism in constructing global formulas.
- Connections to Nest-Tsygan and Tamarkin-Tsygan theorems are established, deepening the understanding of these mathematical structures.
Related Concept Videos
01:25Poisson's And Laplace's Equation
3.4K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.4K
01:09Poisson Probability Distribution
8.4K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
The...
8.4K
01:23Poisson's Ratio
535
Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign...
535
01:24Reynolds Transport Theorem
1.3K
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
1.3K
01:20Region of Convergence of Laplace Tarnsform
697
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
697
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
326
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
326