Problem 13.6

A First Course in String Theory


13.6 Orientifold Op-planes

(a) For an O23-plane the two normal directions \displaystyle{x^{24}, x^{25}} can be represented by a plane. A closed string at a fixed \tau appears as a parameterized closed curve \displaystyle{X^a(\tau, \sigma)} in this plane. Draw such an oriented closed string that lies fully in the first quadrant of the \displaystyle{(x^{24}, x^{25})} plane. Draw also the string \displaystyle{\tilde{X}^a(\tau, \sigma) = -X^a(\tau, 2\pi - \sigma)}.



This one is wrong.




— Me@2019-08-26 10:31:07 PM



2019.08.26 Monday (c) All rights reserved by ACHK

財政自由 1.1
















— Me@2019-08-21 07:40:35 PM



2019.08.23 Friday (c) All rights reserved by ACHK

Physical laws are low-energy approximations to reality, 1.6



too many particles

when you cool down the system, you see something that your equations cannot predict

only by experiment, you discover that you can go to there

the system state goes from one local minimum to another


Since each theory is valid only when near a particular energy local minimum, we cannot use it to predict other local minima (other physical realities). That’s why we need to keep doing experiments that are designed for stress-testing existing theories. For example, one experiment can put a system in extreme high pressure. Another experiment can put a system in extreme high temperature.

Once a theory breaks down in one of those experiments, we see phenomena that we have never seen before. From there, we construct new theories to explain those phenomena.


Once a theory breaks down in one of those experiments, we see phenomena that we have never seen before. In this sense, experimental physics is much richer.

Computational physics goes further in only one direction. Only experiments let you try randomly.

— Me@2019-08-18 07:51:05 PM



2019.08.18 Sunday (c) All rights reserved by ACHK

Literal numbers

All primitive mathematical procedures are extended to be generic over
symbolic arguments. When given symbolic arguments, these procedures
construct a symbolic representation of the required answer. There are
primitive literal numbers. We can make a literal number that is
represented as an expression by the symbol “a” as follows:

(literal-number 'a)        ==>  (*number* (expression a))

The literal number is an object that has the type of a number, but its
representation as an expression is the symbol “a”.

(type (literal-number 'a))          ==>  *number*

(expression (literal-number 'a))    ==>  a

— SCMUTILS Reference Manual



2019.08.17 Saturday ACHK

Multiple dimensions of time

Two dimensional time 5.2 | 二次元時間 5.2


What would be the implications of multiple dimensions of time?

That means the (past) history itself can change, as commonly seen in time travel stories.

But wouldn’t that be the case with one dimension also?

In reality, there is only one dimension of time, meaning that the state of a system keeps changing, forming the timeline. But the timeline itself cannot be changed once formed. In other words, (past) history cannot be changed.

— Me@2019-08-11 04:07:48 PM



2019.08.11 Sunday (c) All rights reserved by ACHK

(反對)開夜車 4.2







— Me@2019-07-30 11:11:42 PM



2019.08.03 Saturday (c) All rights reserved by ACHK