Relationships Between Teachers’ Interactions with Learner Errors and Learners’ Mathematical Identities

2021 ◽  
Author(s):  
Aarifah Gardee ◽  
Karin Brodie
Keyword(s):  
Mathematical Identities

Conformal Field Theory of Free Bosonic and Fermionic Fields

2020 ◽  
pp. 443-475
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theories ◽  
Majorana Fermion ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Bosonic Field ◽  
Conformal Field ◽  
Mathematical Identities ◽  
Modular Transformations ◽  
Fermionic Fields ◽  
The Subject

Free theories are usually regarded as trivial examples of quantum systems. This chapter proves that this is not the case of the conformal field theories associated to the free bosonic and fermionic fields. The subject is not only full of beautiful mathematical identities but is also the source of deep physical concepts with far reaching applications. Chapter 12 also covers quantization of the bosonic field, vertex operators, the free bosonic field on a torus, modular transformations, the quantization of the free Majorana fermion, the Neveu–Schwarz and Ramond sectors, fermions on a torus, calculus for anti-commuting quantities and partition functions.

scholarly journals Theorising the place of emotion–cognition in research on mathematical identities: the case of early years mathematics

ZDM ◽  
2019 ◽  
Vol 51 (3) ◽  
pp. 379-389 ◽  
Author(s):  
Laura Black ◽  
Sophina Choudry ◽  
Kelly Pickard-Smith ◽  
Julian Williams
Keyword(s):  
Early Years ◽  
Mathematical Identities
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