scholarly journals Normal ordering and boundary conditions in open bosonic strings

2005 ◽  
Vol 46 (6) ◽  
pp. 062302 ◽  
Author(s):  
Nelson R. F. Braga ◽  
Hector L. Carrion ◽  
Cresus F. L. Godinho
Keyword(s):  
Boundary Conditions ◽  
Bosonic Strings ◽  
Normal Ordering

scholarly journals Normal ordering and noncommutativity in open bosonic strings

2006 ◽  
Vol 74 (10) ◽  
Author(s):  
Biswajit Chakraborty ◽  
Sunandan Gangopadhyay ◽  
Arindam Ghosh Hazra
Keyword(s):  
Bosonic Strings ◽  
Normal Ordering

scholarly journals Normal ordering and boundary conditions for fermionic string coordinates

2006 ◽  
Vol 638 (2-3) ◽  
pp. 272-274 ◽  
Author(s):  
Nelson R.F. Braga ◽  
Hector L. Carrion ◽  
Cresus F.L. Godinho
Keyword(s):  
Boundary Conditions ◽  
Normal Ordering ◽  
Fermionic String

TWISTED BOSONIC STRINGS AND O(16) ⊗ O(16) HETEROTIC MODEL

1987 ◽  
Vol 02 (03) ◽  
pp. 729-738 ◽  
Author(s):  
G. CRISTOFANO ◽  
G. MAIELLA ◽  
R. MUSTO ◽  
F. NICODEMI ◽  
R. PETTORINO
Keyword(s):  
Boundary Conditions ◽  
Bosonic Strings ◽  
Bosonic String ◽  
Twisted Boundary Conditions

We study the consequences of requiring twisted boundary conditions on [Formula: see text] coordinates of the 26-D bosonic string. In the context of a heterotic model when [Formula: see text] we are led to the tachyonand anomaly-free O (16) ⊗ O (16) model which has been recently discussed in the literature.

scholarly journals Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra

2021 ◽  
Author(s):  
Stjepan Meljanac ◽  
◽  
Rina Štrajn ◽  
◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Heisenberg Algebra ◽  
Higher Dimensions ◽  
Star Products ◽  
Normal Ordering ◽  
Noncommutative Spaces ◽  
Twist Operators

We consider a class of exponentials in the Weyl-Heisenberg algebra with exponents of type at most linear in coordinates and arbitrary functions of momenta. They are expressed in terms of normal ordering where coordinates stand to the left from momenta. Exponents appearing in normal ordered form satisfy differential equations with boundary conditions that could be solved perturbatively order by order. Two propositions are presented for the Weyl-Heisenberg algebra in 2 dimensions and their generalizations in higher dimensions. These results can be applied to arbitrary noncommutative spaces for construction of star products, coproducts of momenta and twist operators. They can also be related to the BCH formula.

CANONICAL ANALYSIS OF NONCOMMUTATIVITY OF OPEN BOSONIC STRINGS

2009 ◽  
Vol 24 (03) ◽  
pp. 239-249
Author(s):  
ZHEN-BIN CAO ◽  
YI-SHI DUAN
Keyword(s):  
Boundary Conditions ◽  
Bosonic Strings ◽  
Dirichlet Boundary ◽  
Open String ◽  
Background Field ◽  
Dirichlet Boundary Conditions ◽  
Canonical Analysis ◽  
Poisson Brackets ◽  
Fourier Mode ◽  
Hamiltonian Approach

Generally, in the presence of an antisymmetric tensor background field, the open string moving with mixed Neumann and Dirichlet boundary conditions will make the spacetime coordinates noncommutative. In this paper, comparing to the flat and static D-brane case studied in the literature, we first generalize the D-branes to be dynamical. And then by using the Hamiltonian approach, through a calculation of the classical Poisson brackets among the Fourier mode components of the string embedding coordinates and a consistent quantization procedure, we show that the spacetime coordinates of the string endpoints in the directions parallel and perpendicular to the D-branes both become noncommutative.

scholarly journals SYMPLECTIC QUANTIZATION OF MASSIVE BOSONIC STRING IN BACKGROUND B-FIELD

2012 ◽  
Vol 27 (13) ◽  
pp. 1250073 ◽  
Author(s):  
A. SHIRZAD ◽  
A. BAKHSHI ◽  
Y. KOOHSARIAN
Keyword(s):  
Boundary Conditions ◽  
Bosonic Strings ◽  
Infinite Series ◽  
Canonical Basis ◽  
Bosonic String

We give the details of symplectic quantization for a system containing second class constraints. This method is appropriate for imposing infinite series of constraints due to the boundary conditions. We use this method for massive bosonic strings in a background B-field and find the correct expansions of the fields in terms of the physical modes. We have found a canonical basis for this model.

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

A digital vocal tract simulator with boundary conditions at lips and glottis

1981 ◽  
Vol 64 (11) ◽  
pp. 18-26 ◽  
Author(s):  
Tetsuya Nomura ◽  
Nobuhiro Miki ◽  
Nobuo Nagai
Keyword(s):  
Boundary Conditions ◽  
Vocal Tract

Exploring the affective impact, boundary conditions, and antecedents of leader humility.

2018 ◽  
Vol 103 (9) ◽  
pp. 1019-1038 ◽  
Author(s):  
Lin Wang ◽  
Bradley P. Owens ◽  
Junchao (Jason) Li ◽  
Lihua Shi
Keyword(s):  
Boundary Conditions ◽  
Affective Impact ◽  
Leader Humility
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