Maple Professional
Maple Academic
Maple Student Edition
Maple Personal Edition
Maple Player
Maple Player for iPad
MapleSim Professional
MapleSim Academic
Maple T.A. - Testing & Assessment
Maple T.A. MAA Placement Test Suite
Möbius - Online Courseware
Machine Design / Industrial Automation
Aerospace
Vehicle Engineering
Robotics
Power Industries
System Simulation and Analysis
Model development for HIL
Plant Modeling for Control Design
Robotics/Motion Control/Mechatronics
Other Application Areas
Mathematics Education
Engineering Education
High Schools & Two-Year Colleges
Testing & Assessment
Students
Financial Modeling
Operations Research
High Performance Computing
Physics
Live Webinars
Recorded Webinars
Upcoming Events
MaplePrimes
Maplesoft Blog
Maplesoft Membership
Maple Ambassador Program
MapleCloud
Technical Whitepapers
E-Mail Newsletters
Maple Books
Math Matters
Application Center
MapleSim Model Gallery
User Case Studies
Exploring Engineering Fundamentals
Teaching Concepts with Maple
Maplesoft Welcome Center
Teacher Resource Center
Student Help Center
Tensor[EpsilonSpinor] - create an epsilon spinor
Calling Sequences
EpsilonSpinor(indexType, spinorType, fr)
Parameters
indexType - a string, either "cov" or "con"
spinorType - a string, either "spinor" or "barspinor"
fr - (optional) the name of a defined frame
Description
The epsilon spinor is a rank 2 spinor which is fully skew-symmetric and whose component values are 1 or -1.
The command EpsilonSpinor(indexType, spinorType) returns the epsilon symbol of the type specified by indexType and spinorType in the current frame unless the frame is explicitly specified.
This command is part of the DifferentialGeometry:-Tensor package, and so can be used in the form EpsilonSpinor(...) only after executing the commands with(DifferentialGeometry); with(Tensor) in that order. It can always be used in the long form DifferentialGeometry:-Tensor:-EpsilonSpinor.
Examples
Example 1.
First create a vector bundle M with base coordinates [x, y, z, t] and fiber coordinates [z1, z2, w1, w2].
Here are the 4 epsilon spinors one can define:
Define some other manifold N.
The current frame is N. Because there are no fiber variables, one cannot calculate an epsilon spinor in this frame. To now re-calculate the epsilon spinor P1, either use the ChangeFrame command or pass EpsilonSpinor the frame name M as a third argument.
Example 2.
The covariant and contravariant forms of the epsilon spinors are inverses of each other.
Contract the first index of P1 with the first index of P2. The result is the Kronecker delta spinor.
See Also
DifferentialGeometry, Tensor, BivectorSolderForm, CanonicalTensors, ChangeFrame, ContractIndices, KroneckerDelta, Physics[KroneckerDelta], KroneckerDeltaSpinor, PermutationSymbol, Physics[LeviCivita], SolderForm
Download Help Document
