File:FeynmanPropagatorWithMass0.2.jpg
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[edit]DescriptionFeynmanPropagatorWithMass0.2.jpg |
English: Feynman propagator, m = 0.2, left/right/top/bottom bounds of image are at = ±2. |
Source | Own work |
Author | Cyp |
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[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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C++ source code - click on "show" on the right to view |
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C++ source code - click on "show" on the right to view |
#include <fstream>
#include <vector>
#include <string>
#include <algorithm>
#include <stdexcept>
#include <complex>
#include <stdint.h>
#include <tr1/cmath>
class Function
{
public:
virtual ~Function() {}
//virtual std::string name() const = 0;
virtual std::complex<double> eval(double x, double y) const = 0;
};
class Identity : public Function
{
std::complex<double> eval(double x, double y) const
{
return std::complex<double>(x, y);
}
};
class Propagator : public Function
{
public:
Propagator(double mass/*, char const *name*/) : m(mass)/*, n(name)*/ {}
//std::string name() const { return n/*"propagator"*/; }
std::complex<double> eval(double x, double y) const
{
double s = y*y-x*x; // y is time, x is a space dimension.
//double const m = 0.0000000001;//.0001;
if(s >= -1.e-20 && s <= 1.e-20)
return 1.e20;
if(s >= 0)
return m/(8*M_PI*std::sqrt(s))*std::complex<double>(std::tr1::cyl_bessel_j(1, m*std::sqrt(s)), std::tr1::cyl_neumann(1, m*std::sqrt(s)));
else
return m/(4*M_PI*M_PI*std::sqrt(-s))*std::complex<double>(0, -std::tr1::cyl_bessel_k(1, m*std::sqrt(-s)));
return std::complex<double>(x, y);
}
private:
double m;
//char const *n;
};
struct Pixel
{
Pixel() { col[0] = 0xFF; col[1] = 0x00; col[2] = 0xFF; }
Pixel(double r, double g, double b)
{
col[0] = std::max(0, std::min(255, int(0.5+255*r)));
col[1] = std::max(0, std::min(255, int(0.5+255*g)));
col[2] = std::max(0, std::min(255, int(0.5+255*b)));
}
//Pixel(std::complex<double> const &val) { col[0] = 0; col[1] = std::max(0, std::min(255, int(127.5+63.75*std::real(val)))); col[2] = std::max(0, std::min(255, int(127.5+63.75*std::imag(val)))); }
uint8_t col[3];
};
Pixel colourComplex(std::complex<double> const &z)
{
double r = std::abs(z);
double theta = std::arg(z);
double y = std::tanh(r/2);
double m = y*(1-y);
double s = m*std::sin(theta);
double c = m*std::cos(theta);
double const q = .5;
double const w = std::sqrt(.75);
return Pixel(y + c, y - q*c + w*s, y - q*c - w*s);
}
class Image
{
public:
Image(unsigned x, unsigned y, Function const &function_, double x1_, double y1_, double x2_, double y2_)
: sx(x), sy(y), function(&function_), /*filename(function_.name() + ".ppm"),*/ x1(x1_), y1(y1_), x2(x2_), y2(y2_)
{
data.resize(x*y);
//#pragma omp parallel for
for(int py = 0; py < int(y); ++py)
for(unsigned px = 0; px != x; ++px)
data[px+py*sx] = colourComplex(function->eval(x1+(x2-x1)*(px/(sx-1.)), y1+(y2-y1)*(py/(sy-1.))));
}
void save(std::string const &name)
{
std::string filename = name+".ppm";
std::ofstream f(filename.c_str(), std::ios::binary);
if(!f)
throw std::runtime_error("Couldn't open file \""+filename+"\" for writing.");
f << "P6\n" << sx << " " << sy << "\n255\n";
f.write(data, 3*sx*sy);
}
private:
unsigned sx, sy;
Function const *function;
//std::string filename;
double x1, y1, x2, y2;
std::vector<Pixel> data;
};
int main()
{
Image identity(1001, 1001, Identity(), -2, -2, 2, 2);
identity.save("PropagatorColours");
Image propagator1(1001, 1001, Propagator(.2), -2, -2, 2, 2);
propagator1.save("FeynmanPropagatorWithMass0.2");
Image propagator2(1001, 1001, Propagator(2), -2, -2, 2, 2);
propagator2.save("FeynmanPropagatorWithMass2");
Image propagator3(1001, 1001, Propagator(20), -2, -2, 2, 2);
propagator3.save("FeynmanPropagatorWithMass20");
Image propagator4(1001, 1001, Propagator(200), -2, -2, 2, 2);
propagator4.save("FeynmanPropagatorWithMass200");
return 0;
}
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 20:34, 26 August 2008 | 1,001 × 1,001 (37 KB) | Cyp (talk | contribs) | {{Information |Description={{en|1=Feynman propagator, m = 0.2, left/right/top/bottom bounds of image are at = ±2.}} |Source=Own work by uploader |Author=Cyp |Date= |Permission= |other_versions= }} <!--{{ImageUpload|full}}--> [[Category:Feyn |
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